Yes, the casual Halo player may not know about Blue Team or any other Spartan-IIs. But anyone who cared even an iota does. I used to have a lot of very casual Halo player friends. Like, they played Halo 2 and 3 exclusively for multiplayer, and didn't even finish the campaigns of either, and THEY know there are other Spartans.

Besides, we've seen other Spartans, and even another Spartan-II in Reach, so it's kindof a null point.