Are CAP members eligible for US Air Force awards like the Air Force Achievement Medal?

No not as CAP members. You may wear ribbons earned in the US armed forces on the CAP uniform but CAP members have a separate regulation (CAPR 39-3) which describes the medals, ribbons, and certificates that may be awarded to Civil Air Patrol members. It establishes the requirements to qualify for them, explains the administrative procedures involved, and prescribes how the medals and ribbons are worn. CAP members are not members of the armed services and thus are not eligible for Air Force awards such as the achievement medal.