If I buy Civ3 Complete, is there a way I can install it so that my current vanilla installation will still work? Thanks for any help.

Not that I've found, but there is no need. Civ3 Complete includes 3 executables that can launch the 3 versions of the game (Civ3 vanilla, Civ3 PTW & Civ3 Conquests). The installer only creates a shortcut to Conquests executable but if you look in the installation folder you will find the others.

Hope that helps.