It can DO over 200hp, but it won't on the 392 unless you swap the pistons. The max load the 392 can take is 5-6psi. 5 being relatively safe and 6 being in the hard yellow danger zone. A P1SC or P1X head unit won't make 200hp on 5psi. You'd need around 7-9psi for that (7 if you find a way to greatly increase the charge air cooling by way of something like a race intercooler) and 9psi will grenade the stock 392. Keep in mind that ProCharger is not going to warranty your engine if it blows up. The general consensus is 5-6psi is in the safe range. Any higher and you're on your way to building a hand grenade.
Now, I used to own a shop that was a certified ProCharger and Diablosport installer and they were one of my sponsors. I know the ProChargers very well. One thing the marketing stuff you're reading doesn't tell you is that if you do get 700 crank hp out of it, it only makes that figure at the extreme top end of your RPM band. ProCharger is similar to a turbo in that it makes boost in direct relation to the engine RPM (which is why ProChargers on Mustangs make so much more HP because they run at a lot higher RPM). Thus, the Hellcat makes most of its available power off-idle, where the ProCharger equipped 392 only makes that power between 5,500-6,100rpm. It offers very little gains below 3,000rpm in the case of the P1SC. The P1X makes gains closer to 2,000rpm. It's also a helluva lot more expensive.
In terms of engine design, the Hellcat has a lower compression rating and different pistons. The 392 has shallow ring lands which can't inherently take much boost. Heck, they have problems with the same issue on larger cams. Another difference is in the rod and crankshaft design in how they allow for crank journal overlapping. This greatly increases the inherent strength of the internals.
And another thing you're missing is that the stock 8HP70 transmission in the 392 is only rated for around 590lb.ft. of torque and something like 650hp. Anything beyond a very minor boost increase is going to overmatch the transmission. Some people swear the 8HP70 can take it, but I can also point out more than a few dead transmissions that failed with a P1SC ProCharger. If you have to swap the transmission, you're going to easily double the price of a build.