running wiring in a new ceiling

I am hanging a drywall ceiling from existing furring strips. There is an inch or more of lath and plaster between the bottom of the joists and the furring. The furring strips themselves are an additional 3/4 in. Can I run 12-2 romex between the joists for recessed lighting by stapling it to the bottom of the joists before I hang the drywall, or must I drill holes in the center of the joists to run the wire? Trying to avoid drilling blind and fishing, also don't want to rip down more lath, plaster, and insulation than necessary.