If I had two charges of the same solid propellant both in the same geometry and casing, and added a de laval nozzle to one, while the other would have just a simple hole for an exhaust, upon firing, would the peak pressure inside the rockets be the same or be greater for the nozzle equipped one? It seems obvious that the latter would be the case, since you feel more of a force if you for example constrict a hose with a finger, but everywhere I look i read that the pressure drops in the constrictions.
"pressure drops in the constrictions" might be misleading. The pressure drops over the constriction. In other words the pressure is higher upstream of the constriction.
The peak pressures are in the combustion chamber, which is upstream of the constriction. All this tells you is the the more the constriction, the greater the difference in pressure between the 'bell' and the combustion chamber.
This is consistent with nozzle -> greater pressure in the rocket.
We know the pressure at the exits is the ambient pressure. The nozzle connected the high pressure combustion chamber(the peak pressure in the rocket) to the outside(surrounding at ambient pressure). So the pressure is 'fixed'. Actually if u add a nozzle here, the pressure difference between the peak pressure in the chamber and the ambient pressure is the power to accelerate the flow speed through the nozzle. The function of nozzle is to increase the exit speed to let the rocket gain a higher speed. The actual pressure distribution in the nozzle depends on the design characteristics like area ratio of the nozzle also depends on if shock wave occurs.