Not really, as the Washington Redskins didn't appear until the team moved to D.C. in '37, though the roots of this team started in 1932.
Much thanks to Hog Heaven for commanding this story, with a very entertaining read on former Redskins Coach William "Lone Star" Dietz, whom is credited with being the inspiration for the team's Redskins name (Dietz claimed Native American heritage). As a justification for an allegedly offensive name this falls short, as the Redskins were the (perhaps less offensive?) Braves before. But as I've argued in the past, for a symbol to be offensive it should at least offend relevant persons, and the relevant persons have to be the ones allegedly targeted for abuse. In this case, the offensive nature of Redskins does not pass muster, as the above link provides evidence that 90% of American Indians found the name acceptable. I don't think the 10% who do find it offensive should dictate to the 90% of the equally qualified American Indians what is or isn't offensive. Which is also to say I don't think the 10% should dictate to the rest of us either. The matter is settled, in my opinion, by the results of the poll (which can change with additional data, which I invite others to provide here).
For the superstitious reader(s), I'd just like to point out that the Boston Braves and then
Washington Braves Boston Redskins ([editor's note, by Skin Patrol] Thanks to sdo1 for catching the error here) never won anything (though the '36 Braves lost the NFL Championship to the Packers). However, immediately after combining Washington with Redskins, Your Washington Redskins won the NFL Championship, 28-21, over the Chicago Bears. I consider that a portentious victory, in more ways than one. We're the Washington Redskins.
But really this post needn't be a defense of a defensible name but rather a celebration of 75 years of our beloved franchise. Happy Birthday Washington Redskins, and I'll drink to 75 more.