I don't agree with Nathan.
You can install and run software/games basically anywhere, except for very specialized stuff.
If a game is programmed well, you will notice nothing but longer loading times. If not, well, you'll see it run like crap.
To the point: I assume you're talking about a USB 2.0 HDD. Keep in mind that you'll cap at around 29MB/s read while (e)sata will give you, depending on drive, around 90-110MB/s. So you can estimate loading times will propably be 4 times as long, if not more.
If you can, use esata. Your notebook might not have an included port, but you can use an esata expresscard to still get the full speed. A acceptable one should be around 30$ I assume. With esata, you'll not notice *any* difference in speed...