I can't answer this question definitively, but I can offer my experiences with escorts. Almost every encounter I've had with an escort, they charge straight in at me. I had one case of a Black Swan Frigate zigzagging as it approached me, but it is possible that it hadn't spotted me yet.
What I have found to be completely consistent is that if you damage an escort enough, they will turn directly away from you and maintain that course for some time. I have observed this behavior with PT Boats, Armed Trawlers, Flower Corvettes, and Black Swan Frigates. I'm not brave/foolish enough to take on anything larger with a deck gun.
The course they maintain is so consistent that I was able to plug a Black Swan Frigate with a 4 meter depth magnetic pistol torpedo at about 3300 meters.
From what I have observed, the only time the damaged ship will deviate from this course is if you bring your U-Boat within about 30 degrees port or starbard (aft) of the ship. At this point I've seen them turn to bring their main battery to bear. I haven't tried this with Black Swan Frigates, as they have a stern mounted deck gun and therefore don't need to maneuver to fire.
I hope this helps. Good luck!
For reference, I'm playing NYGM 2.2 with SH3 Commander 2.6.