I'm considering doing a install of snow leopard.
However my macbook pro battery is broken and I'm using my macbook pro without it. Can I do an install or the battery needs to be plugged in?
You need to have power to do the install, where it comes from doesn't matter, so if no battery is installed, but the power plugged in, then the installation will work.
It even works the other way around.
Sure, as long as the computer boots up, you shouldn't have a problem. If memory services me however running the MBP w/o a battery cuts the speed in half so it may go a lot slower then what you want.
I'd recommend you head over to your local apple store and pickup a new batter - just my $.02