Can I still drive my 1994 toyota corolla if I need to replace the radiator?

You can chance moving it in your driveway very quickly if absolutely necessary (I don't advise this), but I wouldn't push it further than that. The purpose of the radiator is to cool the water that flows through the engine, keeping the engine from over heating. If your radiator blew and all of your fluid is out of the system, it can no longer keep the engine cool. Once it overheats, you risk blowing the head gasket, warping the head or completely ruining the engine altogether. With no fluid to keep it cool, this can happen very fast.

Hope this helps!