Activision bans?

Hey, my modern warfare account was falsely banned months ago, have been playing with this new battle.net account ever since.

Activision have finally unlinked the banned Activision account from the battle.net account with the full game purchased.

My question is;

Is the call of duty ban linked to the blizzard account?

If I link the Activision account that is linked to this blizzard account will I be able to play the game I bought ?