No.  Peter has to stay home to protect MJ even sleeping with her at her home. Any smart villain would kidnap MJ to force Peter to surrender. I would have this scene in Spider-Man 3. Peter tells MJ it’s the first time they are sleeping together and wishes the situation was more romantic. MJ replies that it is romantic with him there to protect her. Peter tells her that if the villains attack together they will overwhelm and kill him but strangely he feels no fear. He tells her that perhaps it’s because of her. It’s the first time fighting villains with her as his girlfriend. He looks at her and tells her how pretty she is and that he is lucky to have her but he is paying the price for being in love with her. He tells her that the holidays are coming and hope he can be with her for Halloween, Thanksgiving, Christmas, and New Year. MJ begins to cry and Peter embraces her. He tells her that the villains are coming and he will fight regardless of their number until he is no more because he is the Amazing Spider-Man and she is his girlfriend