Nope, you're just as screwed using 2.x as you would be 3.x when it comes to games. If something doesn't work, try holding in your two mouse buttons on startup and change the graphics to OCS.
Otherwise, I do know of a disk that magically transforms your 2.x or 3.x to boot into a REAL 1.3 scenario. This is handy if you have a floppy based system only. If you're eventually going to go the route of CD-ROMS and HD's - then back to the top of this thread you go!
Actually from what I recall Kickstart 3.1 was more compatible than 2.x ROMs for old games!