I'm pretty sure you would get lots of interference from running all those wires together like that, and I'm also fairly sure the tiny wires inside an ethernet cable would not survive that kind of power being pumped through them.
Interference-wise it should be fine. Digital data would be far more sensitive than analogue audio.
Distance is also a critical factor, but I probably wouldn't go for anything smaller (higher gauge number) than 18.
Ethernet wasn't initially designed to carry power. PoE applications can transmit ~25w as standard, some new stuff up to ~60w, but I don't know how many wires they are using, I'd assume multiple pairs since the initial spec was 15w.
Either way, it's miles off 260w.
Ethernet is 24awg solid wire, for your 260w power level you should be at minimum using 16awg strandard.
Stranded wire allows more current then solid so this would be more like 24gauge solid vs 12 gauge solid.
I also couldnt image the twisted pair helping interfernece wise
If all you have is ethernet cable you might be able to get away using it but not one run for all the speakers. Using one ethernet cable for each pair or better yet each speaker would probably be OK. You have to be careful to use the same wires at each end. If you make a mistake and it shorts your amp it could damage it severely.
I am using a stand for my TV and with all my equipment in there I had no room for my Xboxes or my dish reciever so I was moving it to one of my cabnents ment for the stuff but my room is set up horribly so there is a closet that I need access to so I can't set it next to my speakers but I also don't want 7 wires running right where I can see them also the wire is a little heavier then normal Ethernet wire