Does QX require a TSO headset?

It is more an issue that the FAA requires it, so yes, every airline requires a TSO headset.

Will have to return the non-TSO Clarity Aloft Santa brought me?

Just have a back up plan if a Fed or "that guy" LCA is in the flight deck.

It's a free game question to ask of the crews, much like the new requirement to carry your glasses if they're required on your medical.

Get a TSO'd headset and you won't have to worry about it.

I can remember when the FAA/QX made it a thing, and it was quite the big deal.

FAA guy: Is that headset TSO compliant?
You: Well yes sir it is.
You: How about that wall?

FAA guy going off on a tangential rant....

Done!

Does the same tactic work during training?
On the line, are their headsets available in the plane for the odd case that the tactic fails?

Just get a compliant headset and be done with it.

My philosophy is to aim for being compliant in every way possible in my daily work routine. Train like you fly and fly like you train. Keep it simple.

Agreed. Just get a GOOD TSO headset. This is one area where it doesn't pay to skimp. You get what you pay for.