Yes, you can definitely have Tiger running on the iMac, which I actually do as well.
The iMac is setup as a dual-boot system with 9.2.1 and 10.4.x.
I originally only loaded 9.x on the machine for nostaligia reasons, but followed that by installing 10.4 to use the machine for some light web browsing.
Upon getting my hands on those CDs, however, It quickly became obvious that those games would refuse to run, even when loaded in classic mode.
Since then, I've just kept it in OS9.