If that happens in Titanfall, you'll still be able to play, but Respawn will only pit you against other cheaters.
You'll know you've been banned because on the private lobby screen you'll see "*FairFight Cheat detected." When you go to join a game, only those that have also been banned will be able to find you, so hopefully your aimbot is better than theirs.
However, what happens if you try and join a game with your pals? You can play with them, but it'll treat them all as banned too for that session.
"When anyone in your party is banned, then everyone in your party will be treated as banned for that play session," said Respawn in an update. "If you are a non-cheater and you invite a cheater friend into a party, you will be stuck playing against cheaters. If you stop inviting your cheater friend, you will once again get to play with the non-cheater population. You do not get permanently tainted just by playing with a cheater - you are only banned for cheating if you are actually cheating."
Unfortunately though, if you've been banned for a real reason, chances are you aren't going to be able to be unbanned and will need to buy another copy of the game if you want to get back in the action against non-cheaters.
Still, if you feel you've been banned unjustly, you can email firstname.lastname@example.org to request a reinstatement.