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).