There were actually two George W. Adgates in Michigan at that time. One, as you've said, was the son of Theophilus, born in NY in 1832, and the other was the son of Thomas, born in Michigan in 1841/2. Both George W's served in the Civil War.
George(1832) married Anna Freeman, lived in Ionia County and lived to be 92. As far as I know, George and Anna had no children.
George(1841/2) married Elvira Cline, lived in Barry County, and had a large family. I am looking for more information about this George and his parents.