Indeed. Looks like some Native American factions something along similar lines too.

Incidentally, I find that the best use for reiters is on the flanks- when the two armies collide send round the reiters round the flanks to lay down a galling pistolade on the enemy infantry, and then charge them in to finish the job when the moment is right. If you try to use normal gunpowder units this way they usually just get trampled down by enemy cavalry but reiters can easily skirmish away. I also find reiters are good for thwarting flanking manouevres themselves- leave them out on the end with the line refused- their range is short enough that they don't distracted shooting at units engaging the centre, but long enough (and their guns powerful enough) that they can inflict pretty crippling casualties at any enemy unit that tries to get around your line.