Running ethernet cable between drywall and cement foundation, and repairing drywall afterwards
It’s not a horrible idea and should be fine.
if it was power you would need a nail plate over the wire but data doesn’t even need an electrical box. 

I usually purchase metal rings that hold the cover plate , you will find most cable installed this way where they punch a hole through the wall, go inside find the hole and cut the opening slip the plate in , much easier than trying to fish the cable through a hole in the old work box.

These devices are called drywall brackets, mud rings, low voltage mounting brackets. Some are metal some are plastic they range in price from .50 to ~6$  

I bought a case a while back of single gang sw-wbf-1 they were maybe .30 in bulk (100 count) some come with screws some don’t but drywall screws work just fine to anchor them in the Sheetrock. 

You may want to cut a small Chanel in the Sheetrock to allow enough space for the wire as it looks like it is attached directly to the foundation.