Here's some history:
the Germans--not even a nation until late 1800s, but there were plenty of German immigrants at this time
the Dutch--the dutch built New Amsterdam (later New York) and established the slave trade.
the Russians--owned alaska and parts of Canda until the U.S. bought it in 1863(not sure if that's exact year)
the French--um... you had to be kidding about this one. French and Indian war? Louisiana purchase?
You weren't wrong on these civs, but here's a short description of them anyway.
Spanish--first to New World and claimed almost all of South America, Central America, and a lot of the now-day U.S. souther territories. And Cuba.
British--You don't need a lesson on these guys. You'd be a moron not to know.
Portugese--small settlements in Souther America, like Brazil.
Ottomans--these guys weren't in the new world at all.
Anyway, an American civ could actually be very powerful lategame. Beyond the War of 1812, America actaully scrambled up to having a respectable army and navy, and won several wars like the Mexican-American one and Barbary Pirates. Americans could get special economy bonuses and early minutemen, both make sense. Thing is, though, American would be very strange since we'd only have 30 or 40 years in AOEIII's timeline.
I think the colonies should be a civ for an expansion IF the expansion extends AOEIII's timeline just a few more decades.