I think if you keep the PSU below 7" or so, it should be fine. Stock EA380 is 5.5" deep. The 120mm PSU fan will be on top, sucking in air from the inside. Shouldn't be much of a problem due to Antec making compartments for cooling so you aren't sucking hot air in.
I don't think an H50 would fit. I use a Scythe Mini Ninja in mine. When I had a low voltage Athlon x2 I just ran it passive. I stuck a fan on it when I upgraded to a Core 2 Duo, but really it doesn't need it since it is near the 120mm fans. I run the stock Antec Tri Cool fans on low, and I can't hear it when sitting on the couch even if the sound is on mute. If I am closer (swapping a disc or whatever), then I hear it if I'm thinking about it at the time.
The video card limitation is because the two HDD bays are in front. There is a tiny bit of room between the motherboard and the HDD bay wall (again, partitioned for cooling) so the card can just barely stick out beyond the motherboard (maybe 20mm???). The other limitation of course is where the PCIe power connector is positioned. A Radeon 5850 might work because the reference design is 9.5" and the connectors are at the end (might butt up against the HDD wall though). The GTX 460 is even shorter so it may be the better choice for that reason. Just avoid cards with the plugs on top. I put a GTS 250 in mine and there was so little clearance that I couldn't put the lid on the case. I had to cut the PCIe connector down and smash the cables a bit to make it fit.
If the guy had really wanted a smaller case and since you would be swapping out the PSU anyways, consider a Silverstone Grandia GD04/GD05. These are like the NSK2480 but besides (IMO) looking better, the optical drive is moved so it overlaps the motherboard RAM area (might conflict with tall HSF though). The HDDs get to hang out in the PSU area. There's still about the same amount of room for video cards that the Antec has, and it has the same two 120mm fans next to the CPU area. It also doesn't come with the PSU. If I were in the market for an HTPC again, these are the cases I'd get.
If you live nearby you can come over and do some measurements on a built NSK2480.