I shall argue that current evolutionary theory (ET) is compatible with the Intervention Claim (IC) that some biological facts about the development of species are explained by one or more miraculous divine interventions at some point in evolutionary history. This implies that evolution is compatible with at least some of the controversial conclusions of interventionist ID.
Now the argument. We can take "evolutionary theory" to have two parts: a concrete and a general part. The concrete part consists of a constantly growing number of specific evolutionary histories explaining the development of particular features of particular organisms, of their geographical distribution, etc., each history having a particular template, in which natural selection tends to play a prominent, but not exclusive, role. The general part will be discussed below.
Two independent arguments now show that IC is compatible with the concrete part of current ET. First, IC merely claims that some biological facts are explained by divine intervention. But the concrete part of current ET does not give evolutionary histories for all features of all organisms. Thus, even if all of the evolutionary histories that form the concrete part of current ET are correct, nonetheless IC might be true, because it could be that an organism or feature for which an evolutionary history is not given by the concrete part of current ET in fact developed through divine intervention. (By the way, in case it is tempting to run an inductive argument from the concrete part of current ET for the claim that every biological feature can be explained without divine intervention, that temptation should abate after thinking about my duct tape parable.)
Secondly, the evolutionary histories involve mutation and recombination, but are mostly agnostic about the precise causes of mutation and of particular recombinations. ET is compatible with determinism, so the histories do not include the claim that mutation and recombination was random or unexplainable. We now know some of the sources of mutation and some of the causal processes involved in recombination, but we would not be so rash as to say that we know all of these sources and processes, and neither would ET be falsified by finding new ones, nor do particular evolutionary histories identify particular causes of mutation or recombination (this particular molecule was hit by this particular cosmic ray, which was emitted by this star, etc.) Therefore, the evolutionary histories are compatible with miracles being involved in the explanation of a particular mutation or recombination event, miracles such as God shifting a molecule around. Certainly, even if some very rare evolutionary history identifies the cause of, say, a mutation event as, say, the impact of a cosmic ray, the history is surely not going to say anything about the particular source of this cosmic ray, and hence will be logically compatible with the claim that, say, God miraculously redirected a cosmic ray to hit this particular molecule at this particular angle.
So we have two arguments for the compatibility of the concrete parts of ET with IC. What about the general part of ET? This makes some sweeping claims, such as that all living things on earth have developed from a single ancestor organism. Now this general claim is compatible with IC, which simply claims that some aspects of the development involved miracles. Now, if ET claimed that all of the biological development from the ancestor organism can be explained in terms of natural selection, then ET would be incompatible with IC. But ET makes no such claim. Indeed, opponents of evolutionary theory are sometimes accused of conflating evolution with natural selection. In modern evolutionary theory, adaptive explanation plays a prominent role, but not an exclusive one. There are other mechanisms involved. To give just one example, one might explain something's arising as a spandrel.
The general part of current ET does not claim to list all of the kinds of processes that were involved in the development from the single ancestor organism to the present biological population on earth. It probably does claim that natural selection was one of the most explanatorily prominent, or maybe even the most prominent one, of these processes. But that claim does not conflict logically with IC, since IC does not claim that miraculous divine intervention was the most important force in biological history. IC does not claim that there was miraculous divine intervention in every organism's history, but even if it were to claim that, this would be compatible with the claim that it is not the explanatorily most prominent part of the development. (Consider a view: God had a plan, and he occasionally made minor tweaks so that things would come out as he wanted.) Thus, IC is not incompatible with the general claims of current ET, if we read these charitably as not including an exhaustive list of the explanatory mechanisms involved.
Objection 1: The general part of ET does include a restriction on the mechanisms involved--it says that these processes are naturalistic.
Response: ET is a scientific theory. It is not a part of a scientific theory to say things like:
(*) "Event E happened by means of some natural cause or other."
It is the part of a scientific theory to say things like:
(**) "Event E happened by means of at least one of the following natural causes: C1, C2, C3."
We can see what kind of evidence is relevant to (**) (e.g., evidence that a random sampling of events like E had them all caused by C1, C2 and/or C3). We cannot see what sort of evidence would be relevant to (*), apart from the bare fact that E happened. Scientific theories have some specificity--they do not simply say that something happened due to some cause or other, and neither do they simply say that something happened due to some natural cause or other. In fact, it seems to me that a decisive argument against calling Intelligent Design in general a scientific theory lies in its lack of specificity:
(***) "An intelligent agent (of some sort or other) intervened (somewhere) in the history of the world (on account of some set of motives or other) to bring about event E."
But (*) is worse than (***) in respect of specificity. We should not, thus, take claims like (*) to be a part of ET.
Objection 2: An axiom in evolutionary theory is that there is no positive correlation between the occurrence of a mutation and the resulting fitness of an organism. This implies that IC is false, since if IC were true, then mutations more likely to make the organism more fit would be more probable, since God would be more likely to miraculously produce them.
Response: Intuitively, there will be more mutations that decrease fitness than those that increase it. (Think of a computer program, and changing a bit of code randomly. Most of the time, it'll either have no effect or the program will crash.) The number of mutations in the history of the world is very, very large. I could estimate this with some data about mutation rates per basepair per generation, but rather than tracking down that data, let's just say it's 1015--it's going to be much higher than that. IC only claims that there are some miraculous interventions. Let's say there are seven (I am only arguing for logical compatibility of IC and contemporary ET, so I can make up a number here). That is going to be such a tiny fraction of the mutations in the biological history of our planet, that it will still be true that the majority of mutations that make a difference make a negative difference to fitness, and hence it will still be true that there is no positive correlation between fitness and mutation.
Moreover, this will be such a tiny fraction of the number of mutations in the history of the world that any effect it has on overall statistics of mutations is going to be well within very narrow error bounds, so any statistical claims about mutations will still be true. I take it we make no statistical claims of the form "exactly x percent of mutations have property P", but rather ones like "approximately x percent of mutations have property P", and variation of seven out of, say, 1015 mutations, given that the total is so great, is not going to affect the truth of such claims.