Worth trying, but the NEO-7M is very cheap and does not give a clean square wave.
Any corrections in edge count to better agree with the satellite will disturb that square wave.

In the discussion I pointed to, it was suggested the NEO-7M was mostly clean at 24mhz.
However, since it is then dividing by two from 48mhz, it can only slow down, by adding
an extra 48mhz clock in there.  It cannot speed up, if that's what the satellite wants it to do.

Best bet is to spend a little bit more money on a better GPS module that has a clean reference.

Jerry