Yes you can!
Ask in the Scenario Creation forum and the experts there will be able to give you some help doing this. It's going to be pretty tough making a Civ 3-style game with the Civ 2 engine, but you can have special units for the different civs. Just give each civ a different tech tree and make the units dependant on techs that the others won't have. This is how you can research the Katushya (sp?) rockets in Red Front, but not the Panzers.