Can I run 32 bit plugins on a 64 bit operating system?

Of course you can. If you're running a 64 bit host, just make sure that it has its own plugin "bridge", which is a sort of adapter, or a sub-host, a small utility that makes the 32 bit plugins usable in a 64 bit environment. But if you're using a 32 bit host in a 64 bit O.S. you don't need a bridge.