Unlocking and unbranding/rebranding are two separate things.
If you flash a branded phone with a generic firmware it will remove any software customizations applied by the vendor but you will still be tied to the original network.
For example on my K800 on the Three network, the internet access menu entries have been replaced by links to Three's own "gated community" network with all their pay content on it. To get to the internet proper I have to go through the yahoo search engine they have generously provided - a search engine that doesn't list all sites.
"Unbranding" the phone (by installing the generic firmware provided through Wotan & Davinci etc.) removes this useless clutter and (as I understand it in the case of Three's K800) makes the internet button configurable to go to some arbitrary URL of your choice.
"Unlocking" the phone however does not change the software installed on it - it just unlocks certain menu entries in the setup so you can choose what phone network to connect to for voice and data connections. Bear in mind you also need an appropriate SIM card programmed with a phone number registered on the network to which you intend to connect.