Can "Me" work as Subject of a sentence?

[essellar]

Not historically or naturally -- as I said in my (much longer) previous comment, it's an academic imposition on English compound subjects, not a natural part of the language. "You and I" may be expected in writing, and many of us who had the construction drilled into us in school (or by our parents) may find "you and me" jarring, but the natural English construct is, in fact, "you and me", as it is in most Indo-European languages.