I've written music (and solved other problems) while sleeping, but it's not a "dream".
I do dream vividly, but It's not musical. Mostly variations of common dreams like it's final exam week and I forgot to go to class during the term. That one never gets old...
You've got a much better application of this than me. I can't extract
any musical value from my sleep.
But strange enough I experience a parallel to your "forgetting to go to class". For me, I'm on campus and for the life of me I can't figure out how to register for my classes. So I end up wandering around from classroom to classroom like some confused wackadoodle trying to solve this problem . . . which I never can. Meanwhile, I have this sinking feeling that my life is wasting away, all because I can't figure out how to register and buy my books! Go figure, in real life I had a superbly rewarding career!

This semi-nightmare has plagued me for years; what I would give for this to be replaced by killer chord progressions and rocked-out bass lines!!!