I don't think much of the wax would make it into a cut.
I was thinking about this and did a few simple experiments using a saw with zero set. Most of wax stays outside actually. All the wax that goes into a cut seems to accumulate in the first 1/8" (or less) of a cut surface and that area looks like a triangle upside down. Depending on how long was the cut this triangle can go all the way to the bottom or cease mid-way. This area definitely won't glue up properly, however there's still enough glue surface for a joint to hold. Obviously a fully glued surface is going to be stronger and I didn't do specific measures to find the difference in strength. I just left it glued overnight and tried to bang it apart with a mallet. It was plenty strong and glue lines didn't look too different, most fibers didn't separate.
Did it because my saw plates are waxed when put back into a till. I was worried that wiping it with just a rag might leave too much wax. After experimenting I just do a few cuts in a scrap first, because all that wax or oil absorbs dirt and looks awful.