Since the following two quotes from the OP seem to disagree, I would like to know if the phone is rooted after these procedures. Can it run Titanium Backup and/or Wireless Tether?
-Can I still receive OTA updates after unlocking the bootloader?
-Answer: Yes. Your phone really does not change at all when you unlock the bootloader. You will still receive updates from Google. Now, if you start putting on custom recoveries and rooting, you may run into issues with receiving OTA updates. The good news is that Google usually releases the system image files for their Nexus phones which makes it a breeze to go back to stock for updates.
5. Once it is done, you have just reflashed the recovery image and it will now stick. You are all done! You have an unlocked bootloader, a custom recovery image, and root access!
-Can I still receive OTA updates after unlocking the bootloader?
-Answer: Yes. Your phone really does not change at all when you unlock the bootloader. You will still receive updates from Google. Now, if you start putting on custom recoveries and rooting, you may run into issues with receiving OTA updates. The good news is that Google usually releases the system image files for their Nexus phones which makes it a breeze to go back to stock for updates.
5. Once it is done, you have just reflashed the recovery image and it will now stick. You are all done! You have an unlocked bootloader, a custom recovery image, and root access!