The carb may need to be adjusted. Also remember that just because it is NOS, does NOT mean it is good. It just means that it sat on a shelf somewhere for 30 years without being installed on a car. Now, adjusting it will be a royal PITA because as a stock GM piece, the mixture screws will be covered by aluminum plugs. You need to remove the plugs before you can make any adjustments. This is done by drilling a tiny hole in the baseplate by the plug (parallel to it's vertical axis), but not through the plug. Then, you use a small pic with a 90 degree head to push the plug out from the back side. It's either that, or you cut the baseplate in such a way that the plug is removed but the mixture screw is not affected. Now, if you do this wrong, you will mutilate the mixture screw or destroy the baseplate, which is the part most of us who run Quadrajets would love to get NOS over all the others. It is the chief failure point of a 30-45 year old carburetor.
As for other possibilities, there are many. The early forays into carburated turbocharged engines of the 70's and 80's were not known for good driveability. Even so, it should be able to work OK. Barring the carburetor, I would look at the intake manifold gaskets, vacuum lines, etc. At idle, that old turbo should not be making any boost and thus it should be working as an N/A. Boost probably does not kick in until around 2500RPM. Unfortunately, I am not familiar with the way that the carburetor and turbo are plumbed in this case. If it is a draw through, you do not need to boost reference fuel pressure. If it is blow through, than you do need to boost reference fuel pressure. As for timing, it needs to be adjusted for the boost level at a given engine load. Deleting that box may have caused some issues. But again, this is pure speculation on my part as I am not familiar with this particular system and do not know it's specifics.