Well yes sort of but no, if the cartridge was not necked down you would have a bigger bore, more room for the gas to expand.
Burn some powder, if there is nothing to prevent its expansion pressure drops to atmospheric quickly, not much happens other than heat generated.
Burn the same powder in a closed/semi closed vessel, pressure generated depends on how much/fast the powder can expand. (BTW to much pressure for the container = kaboom)
Volume of a cylinder is V=pi r(squared) h
So say a .224 dia barrel 16" 3.14159*.224*.224*16 = 2.2551
.30 dia barrel 16" 3.14159*.30*.30*16 = 4.52
.35 dia barrel 16" 3.14159*.35*.35*16 = 6.157 (close to 2.5 times as much volume as the .22 barrel)
More space for the gas to expand in a larger dia barrel=less pressure
Boyle's law - Wikipedia
The law itself can be stated as follows: For a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. Or Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship, when temperature is held constant.
I would guess pressure would be close if you burned the same amount of powder in say a .223 case and an imaginary really long straight wall .22 case of the same volume.
Simply the bottleneck case exists so you have more space for powder while keeping the case length reasonable.
I am ignoring lots of things in the above example but just attempting to try to "paint" a quick picture