Depends entirely on the OS. With 64bit distros they can either be multilib or not, multilib distros have both the 32bit and 64bit libraries installed and so can run both 32bit and 64bit apps fine, on a distro set up like that Quake 4 would be runnable. If you use a strictly 64bit distro you could maybe run it from a 32bit chroot but then you'd need everything installed twice and it sort of defeats the purpose of going 64bit. UT2004 has a native 64bit version on the DVD so either way you're going to win with that game
I recently moved back to a 32bit distro so my Quake 4 and Doom 3 CDs actually got some use, 64bit isn't worth it at the moment IMO and since the performance increase for normal desktop usage just isn't there I don't lose any sleep over the fact I'm only running a 32bit distro.