Probably, yes. If it doesn't, try running Compatibility Mode (right-click the .exe file, Properties > Compatibility > Run this program in compatibility mode for (just choose some option there)). Maybe see if any patches exist for the game.
Oh, with you on Vista, you should install the game as an Administrator. I've heard that a lot, that you need administrator rights to install programs. Of course, if I had Vista, I'd be able to verify this, but I don't so I can't.
95% chance it's going to work anyway.