I looked at many from across the period of the register and didn't find any that carried the names of sponsors. However, the obsessive noting of the child's status as either 'legitimate' or 'illegitimate' continued right through to 1922. Twins were noted, as was the name of the clergyman. I found just one baptism register entry with a later note recording the child's marriage in 1947 and just one (see below) that noted a place name; I'd hazard a guess the latter is the phonetic pronunciation* of the mother's townland/parish of origin).
To access these records, go to galwaywest.rootsireland.ie and login or subscribe as required. If you have a subscription, you can access this particular database by selecting Galway West, Baptisms, and Search (in the menu strip) and typing Galway Union Workhouse into the Full Text Search.
* Annaghdown, on the Galway coast.