There'd be no point to the turbo upgrade at all with the stock IC on there. Sure you COULD do it, but why bother? The tune you get would probably be comparable to what you would get with the stocker, cept maybe less spool and a little more top end.
It won't just heat soak from long use, it'll heat soak in about 15 seconds. I have heat soak issues from my much larger STi tmic on a measly little 16G just on dyno runs. Your WRX top mount ain't gunna deal real well with the VF34.
2015 STi: Still Stock
04 STi, 04 WRX: SOLD