No, it does not.

 

I was questioning whether any service was performed on the vehicle prior to sale as part of the CPO process. If this vehicle went even went though it.
In the p-car world, the dealer will typically get the vehicle caught up on services.
OP has only added 2500 miles since purchase. Maybe that's 18 months of driving, maybe not.
OP has been scarce with details.

 

Would the HVAC stuff be covered though? It does not sound like they are recharging or anything like that (honestly it's not clear to me what they are doing, had never heard of it), but I interpreted it similar to the "fuel injector service" that I was offered many times by my dealer that was really just using some fuel injector cleaner on it and that was not covered by warranty.