Depends. If you factory restore through recovery, you'll be at a fresh version of whatever Rom you have.
If you do a factory reset via the computer, or flash back to stock in Odin, you will likely have to root and unlock the bootloader again.
Sent from my SCH-I535 using xda app-developers app
16GB Blue Samsung Galaxy S III (Verizon)... With a different ROM every couple days....
Custom Built PC- Running a tweaked, de-bloated Windows 8
Dell Studio Laptop- Running Ubuntu 13.04 (sold)