Based from writeups on the web and from experiences of friends, not all games will work using this method even with converters. For one, you won't have a PS button. You'll most likely have to switch off your console to exit a game. If that's ok with you, I don't see any reason why you can't go for it.
Here's one of the tips (taken from Thomas96 of cheapassgamer.com)
"I found a trick that will allow you to play a ps3 game w/ the ps2 controller. I used a Radioshack ps2 to usb adapter, and plugged it into the system, slot 1, then I assigned the ps3 controller to slot one via wireless. So what happens is that the ps2 controller becomes like an extention to the ps3 controller, which allowed me to play some of marval ultimate alliance w/ the ps2 controller. Also, I had to turn the analog function off, as the character kept rolling (when using the ps2 pad) I couldn't get this type of system to work when using a ps2 game unfortunately; I was looking for a way to connect the guitar hero controller to work with the ps3. Later on today I'll be trying it with the actual guitar hero game and see what I actually come up with."
Here's the device you can check out: joystiq.com/2007/05/11/review-pelican-ps2-to-ps3-controller-adapter/
Note that Sony has made some changes to later firmwares (don't remember which) which restricts/limits third party usb devices from working. Be sure to check on this as well before pushing through with your plan.
Do let us know how things go; I have tons of PS2 controllers lying around which I don't mind reusing on the PS3 myself.