Does anyone know if the FRB is considered to be a correspondent under Regulation F (i.e. do we need to monitor their capital requirements and such like we would for other correspondents)...I don't think so, but wanted to see if anyone else had a thought.

No - read the definitions in 206.2 - if you follow "correspondent" to "U.S. depository institution" - it lead back to here:

(a) Bank means an insured depository institution, as defined in section 3 of the Federal Deposit Insurance Act (12 U.S.C. 1813), and includes an insured national bank, state bank, District bank, or savings association, and an insured branch of a foreign bank.