Is it possible for a sim to preform an interaction while posing?

Unfortunately not; once a Sim is being posed with the pose player, it takes up that slot in the active actions and even if you have something else queued, like a conversation about to happen, it treats the pose like it would when your sim is performing an action that takes up all their focus (such as playing instruments, cooking, etc).

I'd say your best shot is to do the pose by name function and try to find an official animation of them actually having a conversation, though it wouldn't be with your own CC poses, just the regular sims default ones. :(