That is a general response which is accurate probably 360+ days a year. However if the park reaches a full closure
nobody gets in regardless of reservation, ticket type, chat screenshot, etc. The
theme park reservations terms & conditions do state admission is not guaranteed. Such closures are typically temporary and the gates re-open eventually, but you could be waiting a while to eventually re-enter.
You will be allowed to leave -- though moving through the crowds to get to the exit may be challenging but not impossible. You won't be forced to stay all day at MK. If your evening ADRs are at another park, you may want to consider simply going to that park for the day.