Yes yes you have
if i reinstall black ops 2 multiplayer on steam, will i get to play online again even if i was banned? or do i have to make a brand new steam account and buy a new black ops 2 game? please let me know asap!
1.q) No.
2.q) Yes.
They keep info about every acc on their servers so it won't change anything if you reinstall game...
New game copy (code), new account, new e-mail.