Unlike in Ubuntu 12.04 where the open source drivers can't even run desktop effects, in Ubuntu 12.10 Unity and Gnome Shell both run well with LLVMpipe as the driver for HD 7750.
Driver performance is, of course, worse than the proprietary drivers at this point but how much worse? Let's see.
The AMD Catalyst driver I'm using are the ones that come with Ubuntu's addition drivers tool.
LLVMpipe fails to run even a single Unigine demo. That's where we are right now. Performance improvements coming in future kernels will hopefully at least run these things. That alone'd be a huge improvement to the current situation.