Yes, unlocking simply removes the network lock and SIM lock that are entered into the phones software when sold to you by the network.
However, if you owe any payments to the carrier this is not removed at all. If your phone is blacklisted, the unlock still remains, however you will only be able to use the device outside of the blacklisted country.
If your device has another type of lock, such as MDM Locks or Knox Locks, the network unlock will NOT remove this & the device will remain LOCKED until the carrier decides to unlock it. Do not order any unlocks if your device has these type of locks.