Hi,
It all depends on what time the MK actually closes. The MK is usually open until at least 10 or 11 every day in June (plus the extra three hours where there are evening EMH), but there is no way of knowing if that will be the case this year.
June hours should be released in about two weeks, so when they are maybe you should should call Disney Dining and ask about a particular date.
Enjoy your trip!