What will happen if Atticus and Tom lose the appeal?

I’m a little confused by your question because there is no appeal in the case against Tom in the rape of Mayella Ewell.  After the initial trial, Tom is immediately sent to the state prison where he attempts to escape.  Tom is shot 17 times and is killed trying to scale the prison fence.  There is a little mystery surrounding why Tom would try to escape.  I think Tom realizes that even an appeal will not be enough to find him innocent of the charges.  Despite Atticus’ encouragement, as a black man, Tom knows he doesn’t have a chance convincing a jury of his innocence because of the institutionalized racism in places like the justice system in the South. If there had been an appeal, and Tom was still found guilty, he would have been sent to the electric chair for the rape of a white woman. Tom also knows that he is leaving his family behind to struggle without him to help provide for them.  Perhaps he feels that he can somehow escape with his family to a better place.  It is not told why Tom tries to escape, but as readers, we know that it is not because he is guilty.