I had both. I would shoo them away just from spawn and i would had peace for quite a while. Another time i would get another back again right away. My guess is spawn rate is based on the overall level of corruption and notoriety.1. I doubt you can shoo them away "permanently" - they seem to simply be taking a step (or two sometimes) back, so if they are already at the "just spawned" position they end up off-screen, but they come back anyway because they go back to advancing on Karryn afterwards.
2. They do have some HP, maybe even the same they would have during normal battles: when my Karryn kicks them for 300-400 HP, they take damage and step back (same as shooing), but remain, yet when she punts them with a 3k+ crit - away they go.
Personally, the point of shooing the goblins away is lost on me: why would I spend a turn on the goblin if I risk gaining nothing (worst case - they remain where they are), whereas I can let them come closer and punt them to make those handshake sessions "goblin-free"?
P.s. What I hate the most about the whole thing is that both actions become unavailable whenever Karryn is Horny. And I have no control over the state because it keeps popping up randomly ever since the "Open Public Toilet" passive which just blank cheques it with "Chance of getting Horny every turn increases". I did NOT expect an effect like that to work anywhere outside the side job required to get it, much less a different side job.You must be registered to see the linksnature of it is...well - the image is damn accurate.
However i do have theory - that is that they react to what Karryn is doing. If they see her working on papers or resting (the multiple turn one) they are like "free real estate". However if you just use breather they tend to leave.
I think this works - shoo them if he doesn't go away - breather then shoo away - then breather again. From my experience that causes majority of them leave.
However why bother? If you have the strip resist book and then equip a title from my experience poor bastards just will keep whacking on the suit and whacking and maybe once per mini-game menage to take the skirt down which is easy to fix. Yea you lose stamina but so you do by using kick or shoo away but you don't lose turns.
As long as you have mind to deal with desires this seemed to work best.