if you submit a new "fresh" Certified Copy Marriage Certificate (the Certified Copy issued less than 6 months), then No;
otherwise, if the age of the Certified Copy Marriage Certificate is more than 6 months, then yes, you would essentially need to get it "apostille'd" (for Thailand it is called legalisation, or authentication)
if you are not going to use an Agent to get a Retirement Extension of Stay at your local Thai Immigration Office = obtain your 1–Year Extension of Stay yourself, then you need to open a Thai Bank Account and get ฿ 800,000.- Thai Baht ( ฿ 800k Baht) in your Thai Bank Account and have that in your Thai Bank Account for at least 2 months before applying for a Retirement Extension at your local Thai Immigration Office
Did you get a Non–O Retirement E–Visa from a Thai Embassy/Thai Consulate outside Thailand or did you get a Non–O Retirement Visa ink Stamp from a local Thai Immigration Office inside Thailand??
Perhaps it's more straightforward to just modify your travel plans to arrive in Thailand a week later and then have sufficient time to transfer all of your Thai immigration stamps into your new passport