Google's John Mueller has stated that exit intent pop-ups do not attract a Google penalty:
https://www.youtube.com/watch?time_continue=746&v=gS4_JH-QqSg
"What we’re looking for is really interstitials that show up on the interaction between the search click and going through the page and seeing the content. So that’s kind of the place we’re looking for those interstitials. What you do afterwards like if someone clicks on stuff within your website or closes the tab or something like that then that’s kind of between you and the user."
Google won't be monitoring the user's full behaviour on your site beyond the initial bounce/non-bounce (at least as far as the search arm is considered, Analytics is, of course, different!), e.g. they won't see that x happened that caused (or appeared to cause) the user to leave.