<p>Yeah, there are people coming out of BFA or BA in MT programs who are singers/actors/dancers but also compose musicals. My D didn’t get training in it but does it. Look at many others such as Pasek and Paul or Nick Blaemire from UMichigan’s BFA in MT program, for example. </p>
<p>But for the OP, if the main interest is musical directing and composing, while you can do that coming from a BFA or BA in MT program, just know that the training is not specific to that and the main training is in singing, acting and dancing and so it only makes sense to do such a program if you want to also train to be a performer as well. Otherwise, go for music composition.</p>