The way you use the word "stain" sounds like some sort of finish with pigment added. I advise against your plan. You would have to be very careful to avoid getting finish on any glue surfaces. Don't count on finish to cover dings/scuffs from clamps. You would also want to be extra careful not to damage finished surfaces during assembly. That takes time and time is your enemy with glue. In any case, do a test fit/glue-up rehearsal before you spread any glue.

A bed frame should be easy/open enough to apply finish after glue-up. I would, however, do finish sanding on hard-to-reach areas before assembly. External surfaces should be only rough sanded- just enough to remove tool marks.

Take a lesson in discipline from this guy. Notice I said "discipline", not technique. He will paint that buggy, so he can sand any-which-way. You cannot. Sanding is my least favorite part of woodworking, and it comes at a time when you're more than ready to see the finished product. Resist the temptation to shave a few hours/days off the project because you'll spend a lifetime noticing 'that one spot'.