No worries. I'm also here to learn.
Iirc Banks was getting around 75HP gains with their turbo kit, and 100HP gains once they added in an intercooler. So on the simplist level, it does mean that cooler dense air does equal more power.
Oh yeah... remember those older Volvos back in the day where they would say something like "840 Turbo" on the rear? Then a few years later, you saw ones that said, "840 Turbo Intercooler". Well, I don't think I've ever seen anyone advertise "intercooler", but I suspect they were doing it because they were proud of the extra power it made.
If you run any supercharger or turbo at a high enough psi without any way to cool the air, at some point it's going to become very inefficient compared to what it would be if you were cooling the air. With low boost applications this isn't as noticeable, but when you start running really high boost levels, cooling the air makes a world of difference.
I ran your question by Charles, and here is his official answer (yes, he got back to me very fast):
"HP at the same boost pressure will be more or less the same except for very slight differences in parasitic losses. The main difference in performance is determined by air charge temperature and how the supercharger's boost pressure varies with RPM. Roots supercharger tend to make more boost and power/torque at low rpms then twin screw superchargers do. So boost comes in quicker and at lower engine rpm compared to twin-screws. Magnum Powers superchargers are high performance roots type that out performs Eaton's M90 because MPx90 is a two cycle machine with long port durations that increases volumetric efficiency (delivering 50% more air compared to the M90) at much lower outlet temperatures. Eatons have short port duration because they have a third cycle that reduces noise. Other advantages the Magnum Powers SC kit for the TJ offers is an intercooler and an independent supercharger drive belt system that allows higher boost pressures than any other on the market."