It's pretty common around here, but we run scads of tag lines on our cats too. I've considered it on the raft, but don't like the idea of passengers and dogs around them, just a bit too much entrapment potential.
There have been a few discussions over the years about their use on cats, search under "tag line".
Never use rope, always use webbing. Webbing has much less chance of getting stuck in between rocks, which rope tends to do. I think the webbing tends to float straighter also, but that may not be a fact. Use polypro, you want it to float, not sink into the rocks.
I am a river, babe - I've got plenty of time, I don't know where I'm going, I'm just following the lines..... - "We are water" by Shaye