Well for the Stage II you will need those upgrades you've listed plus a catback. Once you have all those, you can run the Off the Shelf (OTS) Stage II map from Cobb on the Access Port and have no problems. It even allows an Up-pipe and a crank pulley with that map with no negative effects.
The difference if you get a pro-tune with that setup is perhaps a bit more power, but again as I said, its safe to run those and the OTS map, so no tune is necessary.
I personaly wouldnt get a tune unless you plan to do more to the car, protunes are expensive and to me are only for people in search of serious power. But no, you dont NEED one with that setup using the off the shelf maps, just dont forget the cat-back.
If you start to want more power after this and plan a turbo swap or something like that, a protune is definitely required.
This is how it is for WRX's at least, if anything is different for the STI's, it will all be specified which upgrades are safe to use with their maps on the map notes on this page : http://cobbtuning.com/sti/accessport/index.html
Click map notes for whichever map you plan to use, and all the information you will need should be in there.