By the arc and evolution of Shakespeare's plays, ending with the Tempest (which was solely written by the Bard of Avon without collaboration), I would argue not.
If Mucedorus takes place in one entire day in the classical Greek play tradition, then Shakespeare did not write it. By then, Shakespeare wrote his plays to take place over time. In Hamlet and the Tempest we see or hear about the past and we look forward to a future.
Shakespeare finally reverts back to the one-day form in The Tempest. Also in his swansong, no one dies as the play is not dependent on violence like his earlier works.
Shakespeare wrote about real problems facing Londoners, but disguised them in historical plays so as not to offend the Privy Council or Queen Elizabeth. In Henry V and Julius Caesar, Shakespeare made fun of the monarchy's handling of the once-Catholic holidays.
If there are real problems in Mucedorus that he pokes fun at in camouflage, then the Bard of Avon may have written it. I'll read it and see.
If Shakespeare scholars contend that Gentle Will wrote Mucedorus, so be it. He may have collaborated on it as those London playwrights were friends and rivals. Ben Jonson ridicules Falstaff in "Every Man in His Humour" with his Captain Bobodil character and Shakespeare takes it with aplomb as they were friends. In fact, Shakespeare reportedly played the role of Bobadil on stage a few times for Ben Jonson.
Edit history
= new reply since forum marked as read