Georgia recount is merely recounting the fraudulent ballots since the Secretary of State isn't allowing a full AUDIT such as checking signatures. So, no, such a recount will not show that Trump has won. However, since the Secretary of State did not allow a full audit, could the state legislature (and in the other states) declare that the winner cannot be determined and decline to choose a slate of electors?
Not to mention that the ballot has long since been cast anonymously, so an obviously fraudulent signature on the ballot envelope is a moot point, a lost cause.