I would assume so. Since the first film was a musical, it would be pretty weird to produce a sequel that completely dropped that format.
I assume that they will have Menken back as long as he wants to come back. He has never actually written music for a sequel to one of his previous films before, because all the other sequels were direct-to-video cheapie productions and I'm sure they didn't want to pay him. For a big theatrical release sequel, I'm sure they would though, provided that he finds it creatively worthwhile to come back. He obviously isn't in a position where he needs the money.
Proud of Your Boy is a better song than this iteration of the franchise deserves in my opinion. I thought they should have included it in the live-action remake before seeing it, but when I saw it I was glad that it lives in the higher-quality stage version instead of in that movie.