Yes its a straight fit. IIRC you need the S3's ECU and your old engines MAP sensor
I hope someone can confirm this - Maybe James??
This is not correct, you cannot use the S3 ECU and you don't need to. Also the Map sensor needs to be matched to the ECU, so gti MAP to gti ECU.
Back to the topic, yes you can fit the engine, but why? If you only want a K04 the use of the gti ECU will limit the output as the software written to a gti is limited to the strength of the stock engine. So to gain the same as a S3 stage below the gti you need custom software written specific to your car.
reasons for doing this is if you are considering custom software og going bigger than K04 (which in it self requires some sort of custom software).
I have a cupra engine in my gti so i know