Improving the RAM and the HDD should improve the game.
However, the RAM would have more improvement since the game mostly loads itself into RAM (yesterday SC2 was using 1.45 after a while of playing).
A new HDD should improve up and the speed at which the game loads itself into RAM. I don't know how often SC2 accesses the HDD while playing, but if you are low on RAM, the new HDD should help while OS X pages stuff out of RAM to make room for SC2.
So long story short: the new HDD should help in booting up the game and loading things in to RAM. Once the game is in RAM, I don't think SC2 accesses the HDD that often, but when it does, a new HDD should improve the speed of doing this. The new HDD should also speed up the shuffling around of RAM (but I don't know by how much).
A new HDD from the stock one should bring about improvements across the entire OS X. I still have the stock HDD (waiting until next summer to get a SSD before Lion comes out), but upgrading to 8 GB of RAM has helped me sidestep the problem of constantly paging data out to the HDD which caused massive slowdowns for me (I had 2 GB).
You should be golden getting a new HDD. In a few months after using your MBP a lot, you might consider upgrading your RAM (just watch your activity monitor to see if your system is paging out a lot). SC2 can use quite a lot of RAM when it is able to!
edit: I forgot your question about the external. I don't really know much about this, but if data access is slow to the external, then you could experience some slowdowns at first until the game can load itself into RAM. But someone who knows more about hardware can step in and explain this. Upgrading your HDD is probably the best way to go instead of using an external to play off of.