Of course you can measure the output Z using another VNA. The power levels are low, so you don't have to worry about blowing up your 2nd VNA.

I've connected two NanoVNAs back to back with Coax Ts (to do all 4 measurements with a two port device) What you DO have to watch out for is when the two measurement frequencies happen to be the same - you get a spike in the S11 measurement (which is really measuring the output Z of what it's connected to).

Turn off the sweep on the UUT and not so much of a problem.

And, yes, I suspect that if the input RF switch has blown up, you'd see it in the Z.