Members don't file any family history information to their AOH Divisions.
Some Divisions may have some reminiscences of older members included, for example, as part of a Division anniversary observance but it's not a general policy.
Each Divison does have a Historian but that role is primarily for Division history and not individual members' history.
The best thing to do would be to contact the individual Division to determine what information it may have locally.
Here's a link to the US AOH (I assume you're interested in the US altho there are AOH Divisions in other countries) which lists the Divisions as well as those with websites:http://www.aoh.com/
Other than US census and civil records, information from RC church registers would be available thru the Church the family attended.
Most US Dioceses have websites with parish lists so it depends on where the family lived. Here's the link to the US Conference of Catholic Bishops website which includes Diocesan information for every US state:http://www.usccb.org/dioceses.htm
In cases where churches have closed, the registers generally go to whatever church has taken over the geographic area that church covered.