The Militia rosters survive. When I saw them, they were still tied in bundles as stored in the Adjutant General's office. I doubt they had ever been unwrapped or read since they were used in 1912. There is a printed book, The Massachusetts Volunteer Militia in the War of 1812, printed in 1912 on the centennial of the war. It is quite rare but I do have a copy. I'm in England at the moment but in a few weeks, I will be home and able to look the name up.
The book includes the enrolled militia as well as the volunteer militia so it is comprehensive. If the name is listed, it will also include what unit he belonged to. If the man did not serve in the War of 1812, he won't be there but my guess is that most militiamen of the 1812 period were still in the militia five or ten years later.
jp