Well, she would have needed it, I suppose, if she wanted to receive communion. I have no doubt that she was baptized. Remember, baptism does more than just forgive sins - it incorporates us into the body of Christ, it gives us the power to receive the other sacraments, and it gives us the graces to live our Christian vocation, all things which Mary could very much have used (her sinlessness didn’t mean God didn’t expect her to use the means to those ends). It is to be noted that, given her excellent dispositions, more excellent than any other saint, she would have also received more grace in her baptism than any other saint.
I don’t know if she was at the Last Supper.
Benedicat Deus,
Latinitas