Holy cow, Gut feel says it should work but it might be better to try using the coax to pull some top grade Cat5 cable through the runs - that way you know what you have in place and you can be sure of the quality end to end.
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.
Looks pretty good at 2x$30, I'm thinking this is cheaper than an ethernet over power setup.