Though "possible," painting a home before the property is transferred into your name is unwise for both Buyer and Seller. As an Accredited Buyer's Rep, the first thing that comes to mind are all the "what ifs" that could happen to my buyer-client and/or the property during this time and the "what ifs" something happens to the transaction in the final hours and it doesn't close and my buyer just painted the Seller's house for free. Working for the seller, I would advise against a buyer painting or cleaning or moving furniture in or mowing the lawn...ect...prior to closing due to liability to Seller if the buyer is injured while on the property . . . and the "what ifs" of accidental damage to the property that could occur.
It's a dangerous situation for Buyer and Seller. Though you are understandably excited and anxious to move into your new home, it's wise to wait until ownership of the property is officially transferred to you before you begin painting.