I was wondering if this plugin supports a custom event occurring when the event catches the player instead of an instant battle
A: Unfortunately, not right now. The plugin calls initiateBattle function in every caught action, that start's the battle and handles outcome, but you can rewrite that function only to support another event, sad that there is not any "no code" way to do it, my apologies, I didn't cover that use case.
Also, forgive me if this is mentioned anywhere and I just didn't see it, but is it possible for the player to "escape" from the chaser? Would they have to go to a new map or can you set a certain distance away they have to get after being seen?
A: You can scape from the chaser getting out of his line of sight (manhattan) by a time, also, if you want to make easier o harder to escape the chaser, you can tweak the chase speed config.