Are nail pops under vinyl flooring likely to worsen?
It will certainly worsen. The nails are probably coming up because the subfloor was not glued to the framing. Not only will more nails work up, but the vinyl will very quickly wear through in those spots. 

I agree that this is certainly a warranty issue. If you're not able to get satisfaction from that, you'll need to re-fasten the subfloor and reinstall flooring. I'd probably run suitable screws at 12" intervals on all joists, then fill the dimples and overlay new vinyl. An embossing leveler may be necessary to flatten the texture of the current vinyl.