I agree, it'll probably work.

The impedance of the coax cables will likely be 50 or 75 ohm, whereas the UTP will be 100 ohm. You will need a balun http://en.wikipedia.org/wiki/Balun. Baluns are easy to make, and depending on the cable you've got, probably available off the shelf.

There's 2 pairs in 100mbit ethernet (and 4 in gigabit) - so you'll need 4 baluns for each run (2 at each end).

Personally, I'd pull some UTP through, but it's worth a shot if you've got some time to tinker.