Still at Risk certainly does, as they have an upper level staircase you can use,and many short scenes so it's very easy to sneak someone in. They even had a row "roped off" for late seating.
And Alice by Heart did too. They mentioned no re-entry, but I did see a patron seated after the first or second musical number. Perhaps it's up to the discretion of the house manager.
I will also highly recommend "The Light" at MCC's new space. Excellently acted by its two person cast, it shows why the woman is adamant about not going to the concert performed by a certain someone. Superb set (very fancy house in Chicago) and raw emotions and hurts are revealed. Really gets you into the head of both actors and the struggles they are facing. Runs about 75 minutes including the late start. At that show, I didn't see any late seating (perhaps since it's more of a quiet show and would be more disruptive to others.)