If you mean if Mark with all his current might, money and status suspects to be able to turn Erica around on that point, then I think no, he does not believe that. He knows she is far to integertoo honest. However, I do think that he sincerely believes Erica still being capable of becoming friends with him, whether she changed her opinion or not.
I must admit the ending has a nice touch and it indeed raises this very question to the audience. But I am pretty sure this is just a nice side effect of Marilyn's comment because the film makers had to add a Mark is nice-element as requested by the real Zuckerberg.