I think the issue would not so much be the added manpower. Two regiments more or less will hardly tip the military balance in the West. THe Indians were dead oneway or the other. Also, while the contribution of black troops to the conquest of the West would have been even greater, unless the regiments were instrumental to a great victory (say, the liberation of an abducted First Lady or celebrity), they would most likely simply be ignored by the press. Remember San Juan Hill? Yeah, sure, the Rough Riders. Thus, a slightly larger number of trained blacks with military experience might add to the nervousness of many a white community, but it would hardly be socially significant (what is the annual recruit intake of a 19th century regiment, 200?)
However, if for some reason the Colored Regiments gained fame, that might contribute to a different image created in the mass media. I don't think the 19th century would realistically have supported claims for equality, but if commercial mass media succeed at selling an image of 'the faithful Negro retainer', that might alter public views of lynching, manifest mistreatment or severe cases of inequality. There'd still be stereotyping, but when you look at it, the 1890s' boy story Pathan's growling "Yes, Huzoor" or the Gurkha's "Yes, Sir, Jimmy fetch rifle chop-chop, pot that beggar" resonate with a different kind of respect from "Yes, Massa. Me no want no trouble". (Hell, even the ridiculous Babu "approximatelee eeficient" is nicer.)
You don't treat loyal servants like dogs. You don't go around being perpetually scared of them. If enough people accept the 'new' stereotype of a 'noble, loyal semi-savage' this could result in a less severe, more class-like race relationship, more accomodationist views, and very likely a later and different civil rights movement.
but that's a pretty long shot.