It’s still possible for a headphone’s higher frequencies to affect frequencies within the audible range, whether due to phase interactions or other artifacts. But I kind of doubt whether these things can be predicted. I’d also guess that as much as if not more than anything else these effects would be listener-dependent.
In my own case, I don’t think I can hear above 12k – at least not at normal listening volume – and I don’t pay much attention to frequency response or EQ above that level. But I did give up on it without testing. You might try using EQ above 12k and seeing if you can hear a difference.
The effect you’re hearing at 22kHz is probably due to aliasing. (No offense! 22k is typically lost by your late 20s.) Try the test on this site where you can perform an aliasing test: Extended High Frequency Online Hearing Test | 8-22 kHz