No, Atticus does not think Tom Robinson has a chance. He says this to Scout when she questions him about the case. Scout asks:
Atticus, are we going to win it?
Atticus goes on to say that knowing you can't win a case is no reason not to do the right thing. Even though Robinson will be convicted, Atticus knows he is innocent and will do his best to make sure he gets a fair trial. As Atticus puts it:
Simply because we were licked a hundred years before we started is no reason for us not to try to win. . . .
Scout learns that living with integrity is as important as winning, if not more so. After the trial, when Jem is upset that the jury ruled against Robinson, despite Atticus making it evident he couldn't have raped Mayella, Miss Maudie tells Jem that some whites in Maycomb secretly sided with Atticus. Change happens slowly, she says, and in increments. Even though Atticus didn't win, he made an impression on the community simply because he tried, and that helps lead to change.