But I don't think they'd be working on this unless it could work for real missions too. And with that in mind I took another look at yesterday's launch video. The first thing I noticed is that all nine first stage engines shut off at once, at 3:10 in that video (or about 2:57 after liftoff). This is a departure from past launches (and common practice on other multi-engined rockets) where they've shut two engines down earlier than the others to prevent acceleration from going too high as the tanks empty. The payload is certainly heavier than last time, but this makes me think there was still fuel in the first stage tanks at separation. The first stage goes out of frame briefly but from 3:29 to 3:34 it can be seen firing turnaround thrusters. Then the ground telescope video cuts out and from there all we get is onboard video from the second stage.
So, did it relight?
It sure looks like they tried.