Do I need to update the address registration form for a round-trip visa to Thailand?

Don't. Not when you first check in. If you change your address, you must ask the new owner for a declaration form and submit an updated address declaration form within the next 90 days. 90-day registration form (not required for the first registration), address declaration form (you must ask the new owner for the declaration form and show the updated address declaration form in the next 90 days), and copy the passport, visa and visa extension materials according to the regulations of the regional immigration offices.