I can't comment on the provenance of the shroud (FAT/not FAT), but the similar T1 EMPI shrouds have a pretty bad reputation. When you think about what's happening inside the shroud, you can understand why.
The fan wheel is spinning CW (as viewed from the alternator end). The entire shroud is pressurized, but the "throw" of the fan is directly on top of the 1/2 cylinders, and on the walls or top of the shroud everywhere else. The better shrouds (OE VW, DTM, and most of the 36 hp replicas) have vanes inside the shroud to direct this air over to the 3/4 side in an attempt to cool both sides evenly. The T1 EMPI that looks like that is just hollow on the inside, and I'd suspect this one is as well (since it's made out of fiberglass and I see no rivets).
However - the T4 has a reputation for being super easy to cool, so maybe it'd work just fine. I wouldn't do it, but I tend toward overkill.
As far as the car: all of the parts bolted together on this car seem to total about 1/4- 1/2 of what the parts by themselves are worth. That says something about what most people think of it. But since you told us not to disparage the car,
I'm sure it's a great cook and has a lovely personality.