I thought about this a bunch a number of years ago. I'm not sure I ever came to a definitive conclusion. But, my thoughts on this are the following:
1) For design of the lateral force resisting system, composite action should be ignored. This is because I don't believe there is any guidance on how to do "seismic detailing" of a composite beam. Which means I focus on the moment connection design the same way I would for a beam that was non-composite.

2) I don't believe there is any problem with having studs on top of the beam that connect it to the deck as long as those aren't in the protected zones of the connection.

3) I see no reason why you couldn't use "composite action" to evaluate the beam for deflection. I would probably do that assuming the beam is a simply supported composite beam or a non-composite moment frame beam. However, I can see how another engineer could want to use reduced composite action on the moment frame beam based on the percentages of the beam that are in positive vs negative bending. I believe AISC has some discussion of this in their commentary. My impression was that this AISC commentary was more intended for the back span of a cantilever beam. But, I see no reason why it couldn't be used for this case too.

I agree with Josh. Physically a girder can be both composite and part of a moment frame. AISC wouldn't have the protected zone stud limits for SMF were that not the case. The only real question is whether or not one can take advantage of the composite action for lateral design if they wish too. Like Josh, I feel that there probably isn't much to be gained by attempting that. At the same time, for a low ductility OMF, I'd be surprised if there were not some way to do it and stay street legal.

Thanks a lot to both of you!