Pretty much
You will probably find your 50T outer ring is next to useless on a cross bike though.
Wouldn’t go for BB7’s, the mechanical disc brake game has moved on… Go for TRP Spyres, or even better, the mech/hydro combination TRP HyRd instead. A caliper with only a single moving piston works ok on a road bike, but for anything that ventures off road into the dirt it’s less than ideal.
EDIT: FWIW use the SRAM over the Sora. I find that off-road, the fact that the brake lever doesn’t move is much more confidence inspiring when braking over bumps. Also SRAM 10spd road stuff is interchangeable with MTB, so you can run a 10spd SRAM MTB rear clutch mech which will then also give you the ability to run anything up to a 40T big cog cassette comfortably…