As far as I know there's no definitive answer yet. I guess we're waiting for someone to actually obtain the required cable and successfully fit a second drive in a 2011 mini with Radeon 6630M. It certainly looked like there was room in mine when I fitted my SSD the other day. It had the space under the HD just like in the teardown of the Intel-graphics-only mini. As soon as it's confirmed possible I'll be adding a second drive to mine for Windows.
I have a mid-2011 i7 Mac mini and I've replaced the HD with a (non-Apple) SSD. It's working great. When I use iStat Menus to view the sensor readouts for temperature/voltage/fan speed, etc, I note there is nothing listed for HD temperature. However, I have removed the Apple HD - as I said - so I can't tell you definitely without replacing the original HD whether Apple use a thermal sensor built-in. On the other hand, I can assure you that the fan appears to work just fine. It idles silently, and turns the room into a wind tunnel when Flash is being played (all functioning normally, then :D ).
Yes, you can. I'm typing this on such a machine, with an SSD replacing the original HD. You can do this by following along the iFixit teardown, plus a bit of common sense and wriggling components in sensible ways (it's tightly packed in there). You won't go near the Radeon chipset, so the steps for fitting an SSD are the same whether yours has discreet graphics or not.
Just in case it's of interest to anyone: I have now replaced my iMac with a mid-2011 Mac mini, dual-core i7 2.7GHz, 8GB RAM and I've moved the same SSD into that. It works fine AND boots various Windows-y volumes, like a Windows installation drive etc. So I guess the issue was something in that particular Mac after all.
David Hodson's answer is half-correct. It *is* just a standard HDD swap, however: 1) A guide to installing Leopard or Snow Leopard won't help because the 2011 Mac Mini won't run any OS X older than Lion. You *could* use another computer to install Lion on the SSD before fitting it, or wait for and buy the USB-stick version of Lion. However… 2) The good news is you should be able to just fit the SSD blank. I believe the Mini's "Internet Recovery" will allow you to connect to Apple and download and install Lion directly. All you need is your WiFi key or Ethernet cable :)