Is my faulty AC covered? AC shop said refrigerant is full.

Hello, that VIN is not valid. Check it and respond. There is an extended warranty on some 2007 - 2011 CR-V's for the compressor clutch. Have to check the VIN to see if it applies, and must be under 100,000 miles or 7 years in service. So, it will depend on your in service date when the CR-V was new, and your mileage at the very least. Of course, this might not be the cause of failure either; proper diagnostic testing must be performed to find out what has failed first.