Honestly don't know. . .
It totally depends on the game and what the built in code is. As I said, I've installed older games on an internal partitioned drive D: with no problems. Some other games will not install if you try to change the target to anything other than C:. Who knows what the newer games will or will not do? Here is a popular gaming site, maybe you could join the forum and get some information there http://www.gamespot.com/
Why not go ahead and get the new external drive, move all your other "stuff" to that drive to free up space on the C:?