I don't know if there is any connection but I thought I'd try.
I have a John Thompson ancester who was said to have been farming in Grant County as early as 1840. I don't know where he was born. His son, Charles, was born 1831 in WI, but I'm not sure where either. Charles and his family stayed in Grant County near Patch Grove / Mt. Hope until the 1870s when they headed for Iowa and North Dakota.
You alluded to your ancester as perhaps having a Thompson mother. There appear to be several early Thompson families in SW Wisconsin in the 1840s and 1850s. Do you know any more about her Thompson line?