Apparently, yes. According to the (canon) Star Wars: Battles That Changed the Galaxy factbook, Wedge's destruction of the power regulator was instrumental in the reactor exploding.
A Chain Reaction:
Wedge Antilles destroyed the Death Star's power
meaning that when General Calrissian opened fire on the reactor itself it suffered a catastrophic collapse. A huge explosion was
This is echoed by Wedge's Biography Gallery on the StarWars.com website
Once Han’s commandos brought down the shield generator protecting the
Death Star. Wedge flew into the battle station's superstructure. He
followed the Millennium Falcon into the heart of the Imperial
superweapon and fired a proton torpedo into the main reactor’s power
regulator, helping start the chain reaction that destroyed the
The implication seems to be that if the reactor could regulate its power properly, it wouldn't have exploded when damaged, it would have just shut down or fizzled.
The Official Star Wars Fact Files #113 is also similarly certain that both elements were required in order to create the devastating cascade failure that blew up the Death Star II. Interestingly, it refers to each of the attacks as 'laser fire' rather than 'missile fire', but we can probably chalk this down to writer's error.
When the Rebels attacked the second Death Star, they targeted the north tower first. This contained the power regulator, which channelled off excess power. If this facility had remained operative, the Rebels' laser fire could have been absorbed and its assault would have been unsuccessful.
With the north tower destroyed by laser fire, the Rebels made a frantic escape. Their assault had started a chain reaction, releasing the reactor's enormous power which soon destroyed the second Death Star from within.
The floor, ceiling and walls of the vast chamber were
covered in power conduits that carried the energy from the reactor to
various parts of the battle station. These were one means of absorbing
power surges from the reactor, Another was the power regulator built
into the north tower. This extended from the side of the tower and
served to channel off excess power. It was this feature that the Rebel
strike team hit first. If it had been left intact, the power regulator
could have absorbed the energy of the Millennium Falcon's lasers. As
it was, just a few laser blasts set off a catastrophic collapse in the
central contact space. This brought the north tower crashing into the
chamber. From this point' on, the Death Star was doomed. Within a few
seconds, a chain reaction released the vast power within the reactor,
and the battle station was reduced to ashes.