Yes, do that...
Our school Macs have either Safari or Camino; neither one of them works very well. And Firefox on a Mac is very much like Firefox on Windows.

Just be sure to follow the given directions very carefully when you first install it; I was stupid and ignored the last (and most critical) step because it didn't make sense to me (a Windows-type person), and my install disappeared after I booted the machine a couple of days later...