The HDHomeRun stream would be already encoded as an mpeg stream so there is no need to encode on the RPi. I suspect where you would run into problems would be the MySQL database updates that MythTV does for seek tables and program guide information, especially if you are using USB or network connected storage since the RPi connects to the network through USB (the ethernet chip is USB connected on the board if I recall correctly). Essentially you would have the mpeg stream from the HDHomeRun coming in, the disk reads for the recording you are watching coming in, and then the mpeg stream going out to your frontend AND MySQL database queries trying to access storage all through the poor RPi USB.
I'm not saying it can't be done, but I suspect you can't record more than 1 show at a time, and might not be able to watch and record without issues.
1Another relevant bit of information: the actual TV stream would be coming from an HDHomeRun device on the network. – Josh – 2012-10-19T19:03:10.560