I suspect in the end the answer to my title question may be positive, but I want to run through an argument that makes it problematic that a perfect act-utilitarian, i.e., someone who always figures out the maximum utility and acts in according to it, could make assertions. I am making no claims of soundness or validity for the argument.
Making assertions is a norm-governed practice. An essential part of what it is to engage in a norm-governed practice is to accept the norms as applicable to oneself. What exactly the norm of assertion is—what conditions are such that making an assertion that p is appropriately—is controversial. Proposals made have included truth, belief, justified belief and knowledge. All of these have something to be said for them. But the following does not: "The norm of assertion is the maximization of utility." The practice of uttering that which the uttering of maximizes utility is not the practice of assertion. The perfect act-utilitiarian is governed by the norm of utility-maximization in all actions. Therefore, she does not accept the norm of assertion. Therefore, she does not engage in the practice of assertion. Therefore, she does not make assertions.