Two different entities.
Yellow Tabien Baans are obtained by registering your address with the local government under the Civilian Registration Act, whereas for Immigration you register your address under the Immigration Act.
Sure, if you had a YTB, Immigration would take a copy if offered, but they predominately want copies of the house owner/landlords Blue Tabien Baan, Thai ID card and if applicable a rental contract as proof of your address.
In your situation, what would be the advantage of obtaining a YTB and ID card?
Purchase a new vehicle, obtain driving licence, in which case the address on the registration logbook and driving licence would be different from your actual residential address.
Many Amphurs now require an Embassy certified copy of your Passport, translated to Thai, then legalised by the MFA. Some may also request the same of your birth certificate detailing parents names, which are entered in the YTB.