I have a Colt cut carry handle that I picked up off the board and was planning on using it on my BM SL upper. I also bought a NIB BM CH which I'm currently using.
There is a height difference between the Colt and CM carry handles. I don't know if Colt ever made non-M4 compatible CH's, but do know that Colt is making the M4 front sight assembly taller than the non-M4 sight assembly. Apparently if you crank up the front sight post to almost level with the top of the "wings," it will zero.
I have not tried to zero my Colt cut CH on my BM upper, but could get you some measurements tonight (including a Colt CH that came with an M4 marked upper). Zeroing it shouldn't be a problem if you are okay with the front sight post being higher than normal.
YMMV, and others who have done this will obviously have better information than I do. Let me know if you want those measurements.
EDITED to add that I'm certain that Chuck has it right. He's forgotten more about AR15's than I'll ever know. I was bassackwards.