When you put a hard drive into the PS3 for the first time, it gets formatted - so no. The PS3 itself doesn't support external hard drives for games like the Wii U and Xbox One do. You can back data up to a external HDD, but you can't play games off it. This means you're going to want to get both an internal HDD and an external HDD to back things up to.
You can take it out and put it in a slim, but you will have to wipe it unless you can at least still booth the fat to do an HDD transfer. Had this exact situation happen to me. But thanks to PS+ cloud saves it wasn't much worse than having to reinstall everything.
Hmm, alright, thanks for the info guys. I think I'll just stick with the 60GB for now and download/delete as I play. I have PS+ so I can keep all my saves backed up there.