NO! Be very careful if you are dealing with used turbos. K03 refers to the housing size only. K04 is a housing size. Garrett 15 is a housing size. Garrett recently changed their naming system so now it would be something like G1517 or G2520 instead of GT-25. A gasser's k03 is not the same as a tdi k03, the housing may be similar but the turbo wheels are different sizes. This is because their spool up is for a different amount of gas and higher in the rpm band and is designed for less boost. A TDI turbo is designed for lower rpms and higher boost at lower rpms.
If you want to swap in a VNT turbo, it'll bolt up but the mounting is a little different, you need a new downpipe, maf, n75, ecu, and I think a motor mount.