I don't think A/C units are typically considered continuous loads by defintion, but the circuit must be sized to the MCA which is not less than 125% of the rated -load current (440.32) so it is the same
The circuit ampacity would normally be determined by the MCA listed on the nameplate.
If a load is 40 amps and is continuous then you would need a conductor rated at 50 amps, or a #6 NM.
There is no problem in your installing a #6, but I think most inspectors would look at the A/C unit MCA and assure the cable installed was adequate for that number.