It seems that the answer has to be negative—isn't the idea utterly absurd? But suppose that an A-theory is true and Fred is a timeless being. Let W be the property of being (timelessly) in a world where a war is (presently) occurring. It seems that on A-theories this is a genuine property, and it was true in 1944 that Fred then had W and it is no longer true in 2008 that Fred has W. So it seems that Fred has changed in respect of W. The B-theorist is apt to deny the existence of such a property as W, and instead talk of the family of properties Wt of being (timelessly) in a world where a war is occurring at t. It was true Fred in 1944 had W1944 and it is true in 2008 that he does not have W2008, but that is not a change, since likewise it was true in 1944 that Fred had not-W2008 and it is true in 2008 that Fred has W1944.
So, if the A-theory is true (or at least if one of those A-theories is true that allow tensed properties like W), it follows that timeless beings change. Of course, the change is extrinsic. But even extrinsic change is puzzling in the case of a timeless being. Look at it from Fred's point of view. Does he or does not have W? It seems both, but that is absurd. In the case of a being in time, we would say that the question is ambiguous—does he have W at what time? But we cannot disambiguate this from Fred's point of view.
Here is something an A-theorist might say. She might say—in fact, I think that on independent grounds she should say it—that at every time, a different world is actual. (Right now, a world without a present world war is actual. In 1944, a world with a present world war was actual.) Then there is no contradiction in Fred's both having and not having W, since since in one world (the 1944 one) he has W and in the other (the 2008 one) he does not.
If we take this route, then the "objective change" that A-theorists are enamored of will be a movement (an orderly one) from one world to another. But Fred undergoes that movement just as much as you and I—in 2005 he was in the 2005 world, and in 2008 he is in the 2008 world—though there is a difference whose significance I am unable to evaluate at present (Fred exists timelessly in both worlds, while you and I exist presently in both worlds). It seems, then, that Fred undergoes objective change, while being outside of time. That seems absurd. Moreover, if we take this route then the following conceptual truth becomes really hard to account for: Nothing outside of time can undergo intrinsic change. But why can't Fred have one set of intrinsic properties in the 1944 world and another in the 2008 world? And if he did, then he would be changing in respect of intrinsic properties.
If the above is right, then it seems that what the A-theorist needs to do is to deny the possibility of timeless beings. This has some interesting consequences. If time began with the big bang, and if we are realists about mathematical entities, then the number 7 is about fifteen billion years old, give or take a couple of billion, and if time were to come to an end, then the number 7 would cease to exist. And once we've allowed abstracta to be in time, why should it be any more absurd to allow them in space? I do not know if these kinds of considerations form knock-down arguments against the view (and hence against the A-theory, if the A-theorist needs to go there), but they are worth thinking about.