I downloaded and tried R1Q2 out with GameHost. It works fine if you pass the "-oldconsole" parameter, but there doesn't appear to be a way to do this without replacing the whole command line or editing Games.ini.
For optimum compatibility with GameHost, please download these modified GameHost files:http://www.r1ch.net/stuff/r1q2/download/r1q2-gamehost-update.zip
Shut down GameHost and extract the above files to your GameHost directory, overwrite the existing files. GameHost will now use "dedicated.exe" when looking to start Quake 2, so be sure you have dedicated.exe present! I have also updated the Quake2.GOF file so that a number of R1Q2 parameters can be configured directly inside of GameHost: