It will, yes. However, it may be possible for the Sathanas to get the Phoenicia's hull from 4% to nothing faster than it takes for the departure cue to trigger. On lower difficulties, the Phoenicia usually stands a higher chance of jumping out because enemy beams do less damage. Having played FS2 on Very Easy for most of the past few years and cheating on Insane for much of the rest, I've observed that, on Very Easy, the Hecate usually jumps out with around 3% hull, but on Insane, it always jumps out with 1% hull.
I have never personally seen the Phoenicia being destroyed by the Sathanas, so I assume the performance of the computer running FS2 comes into play as well.