I had issues with the EGR pipe not reaching the revised location of the throttlebody on the adapter. I also had problems with it hitting my valvecovers. Fixed that with a 3/8" spacer. It kind of rubs my hood liner but nothing major.
i had the valve cover issue but I have fox covers. Then I put a 1 inch spacer on it then the egr tube didn't reach but you can buy and adapter though 50resto that kinda fixes that problem. But I don't have a stock hood so that part of it i don't know
i have the track intake (same thing) and i had the egr tube problem with the valve covers. If you know how to weld you can cut your tube and make-shift and new. I went with the 1 inch spacer and had to get a new hood. No clearance probs now. I still had to make a new egr tube though. Good luck. But to answer your question the intake will fit under the hood.
I had the street heat, no spacer, stock hood, and with stock valve covers and had no clearance issues. The EGR tube has some ribbing designed to flex and stretch.
To change my valve covers I added a 1 inch spacer, extended the EGR tube by an inch (cut and weld), and modified the underside of my stock hood until I got a new one.