Me has the *ahem* version game files played till level 24, have bought the game, can I copy the files over to the steam folder and do the 'integrity' check and expect the game to work through steam?
Yeah, it will work fine. I did for many steam games including BL2. Follow the below steps:-
Activate the game key in steam, if the download starts, stop it.
Goto Game Library, right click on BL2 and Click Delete local data.
Then goto steamapps/common folder
Create a folder named Borlderlands 2 and paste the files except Binaries, as told by sam.
Then install the game from steam.(Click play button)
It will show progress like , Discovering local content etc.
Remember it will still download some data and in steam it will show like 5-6 GB to download, but after some time the progress will jump . for example it will go directly from 5% to 90 % like that.