After some research today I feel confident in debunking the myth that the 11th Wisconsin was dominated by Irish recruits; please do note that I am German/Irish.
Looking through the muster roll I would say, with just a glancing guess, that maybe 25% of the regiment might have been Irish or born in Ireland. And I think that is a generous proportion.
I also found some good secondary sources that also clearly support my position that the 11th Wisconsin was most likely a very diverse regiment, and not dominated by any one group.
The only regiments from Wisconsin that appear to have been dominated by a specific group were the 9th, 26th, and 45th who were made up mainly of German recruits; the 15th was Scandinavian; and the 17th Irish. No mention of the 11th.
The only group that we know for certain dominated the 11th Wisconsin ranks were wheat farmers.