Not quite
To be clear, unlocked means no SIM lock. This is not the same as unbranded (generic samsung, not carrier branded).
SIM unlocking a device does not change the software version on the phone. Its the software on the phone that dictates where the update comes from. If that software is carrier branded, it comes from the carrier.
Sure, if you buy an unbranded device, it will be SIM unlocked but these terms are in no way synonymous.
For example, early 3UK s3's were not SIM locked but still carried 3uk software.