Got a tape measure??
The inlet to the back box on a stock exhaust is 1.75".
The inlet to an STi version 4-6 back box exhaust is 2.25".
The tips are much larger. I haven't measured them myself, but look at your inlet and outlet. They aren't the same size. the inside diameter of the STi tip is the exact same size as the outside diameter of the stock tip (fits inside it).
If this has a midpipe you'll be fine otherwise you can get a custom one made to fit the back box's flange, not need to touch the back box inlet. SPD tuning sells/makes midpipes to fit these back boxes.. might want to contact Mike if you need help.