COR responsibilities for accepting supplies/services includes accepting items -
that conform to contract requirements?
Yes, if they've been delegated that authority/responsibility. The Contracting Officer must decide what duties to assign and delegate to a COR. There are common and typical duties which are delegated but none that are "automatic". Each contract or order stands on it's own.
See FAR 1.602-2(d) and focus on 1.602-2(d)(7); you will have to check your Agency (FEMA) FAR supplement to see if has additional implementing or supplemental guidance.
If the COR is delegated acceptance responsibility; then yes the COR can ONLY accept items that conform to all contractual requirements, see FAR 46.407 (and again, your agency supplement).