While I think tor and something like torchat is good in theory, its big negative in reality is that the speed makes it unusable most of the time. Not to mention if you are altruistic and plan to run a node, you also run the risk of the FBI knocking on your door for someone who used your (exit) node to upload their kitty porn (the exit is not encrypted).
And if you do run that exit node, you can sniff what people are doing (so there goes the anon part).
Tor was pretty bad for web browsing - latency and pages requiring multiple resources meant that pages took forever to render. But how much is being transfered or rendered with chat? Not very much. IRC is usable even over atrocious connections. I rather imagine that textual chat over Tor would work fine.
and I say this as someone who ran a Tor relay on his Xbox to get 1 hop out of the way
And if you do run that exit node, you can sniff what people are doing (so there goes the anon part).