At that altitude I think they could. I would be much more worried about the SRB motors. My guess is those are replaced with new ones. Good point, I had forgotten about the thinner air at high altitude. I would thing they would check the viability of the SRB before test firing, but then again, the SRBs on the Challenger were checked as well.
Here's to a successful test.
From what I have read, one reason the Phoenix was retired was that that the SRB (as all do eventually) is develop cracks in the propellant. This makes for an uncontrolled environment and sometimes it goes 'boom' rather than 'push'