Answer:
The rules on advertising including Member FDIC are at 12 CFR 328. In 12 CFR 328.3(d)(3), one of the exclusions that do NOT require Member FDIC is "signs or plates in the insured depository institution offices or attached to the building or buildings in which such offices are located". So I think you'd be OK in omitting that for a sign visible only inside the bank. Equal Housing Lender rules don't have such an exclusion, so if you mention loans that could be secured by a dwelling, you'll need to include that. Same for the Not, Not, May disclosures if you mention investments.