Will I lose my unlock if I unroot galaxy note i717?

[AC Question]

So here is the thing I got my phone unlock to use with other carriers via a computer (i didn't get an unlock code) and i didn't know it was rooted untill now but i always wonder why it would always run slow and found out the at&t rethink logo that comes when you turn on a phone doesn't show it shows an X and i found out data service don't work but everything does as wifi does too. So I want to unrooted but I don't know if that will make me loose my unlock and i don't have a code to put in if i lose the unlock please help. I found how to unrooted and saw that I will be installing the factory rom as well as the latest android version from at&t available for my phone but im more worried about losing my unlock. Thanks