Members generally didn't have to document their Irish heritage. Membership requirements were a) practicing Catholic and b) Irish or Irish descent. Each member had to be sponsored by another member who knew the prospective member. Generally at that time the local Division was made up of people who lived in the local area and who already knew each other from the community or church. Local Divisions would have a historian but it's wholly dependent on the Division what records of the Division might survive and what they may be. Some Divisions have done histories.
There isn't a website for Division 1 in Detroit. You might want to contact the State Board to find additional information on that Division. Here's the link to the State board: http://www.michiganaoh.com/
To find where your ancestors came from in Ireland you need to check the following: a) US Federal Census records for the family back to the time the emigrant arrived in the US. Those records will help you find the other records you need to research which include: b) the original emigrants civil and religious marriage and death records, obituaries, tombstones, cemetery records, wills and US naturalisation records. The Petition for Naturalisation/Declaration of Intent generally has more information on the emigrant.
In addition to the emigrants' records, their children's civil and religious birth (baptism), marriage and death records may include where their parents originated in Ireland.
There are generally no surviving census records for Ireland for the 1800s and civil registration didn't start until 1864 so church registers for the townland, civil parish and county where your ancestors originated are the source for family information. There's a list of all the townlands and civil parishes in Ireland at http://www.seanruad.com
and just select your county of interest. Here's a map showing the counties of Ireland: http://philnorf.tripod.com/ireland.htm
Once you find the townland, civil parish and county where your ancestors originated, you can check to see if any of the parish registers have been microfilmed and are available through the Latter Day Saints - the Mormons - Family History Centres. Some counties also have Heritage Centres where they'll research the church registers fee-based.