Is there a method available to have the plugin pause and wait for a user to click some object, then continue? Or does all user interaction have to happen before/after the plugin is run?
No, there's nothing provided to do that. You might be able to hadck something together to let that happen, but it'd be mighty fragile. Without Illustrator's help in preventing the user from changing tools or running something else, I'm not sure how'd you force them to click on something and then have it inform you of the event.