No, it is not correct and is a common error with a compound subject. The correct pronoun is I because it is part of the grammatical subject and requires the nominative case. However, people who would never think of saying, "Me is going to the movies," will say, "Mary and me are going. . . ."
What about "Give it to Mary and me"?
This is correct. The pronoun me is an object – specifically, the object of the preposition to – and therefore is in the objective case. What is incorrect is "Give it to Mary and I." Once more, people who would never dream of saying, "Give it to I," tend to make this mistake with compound objects. And, by the way, it is also incorrect to say or write, "Give it to Mary and myself." A -self pronoun (i.e., an intensive/reflexive pronoun) always refers to another noun or pronoun in the same sentence that denotes the same individual or individuals.