You can claim the pump is important, but I routinely get bigger and stronger while getting little pump during a workout.
There may be some supplemental effect of getting a pump in a workout, but the real deal is fiber microtrauma from percentage of 1 rep max and total workload.
Seen a million guys get great pumps, but not get bigger and stronger.
There are a couple national level powerlifters at my gym that are fucking yoked that compete natural and they rarely go over 5 reps and take lots of rest between sets. They joke about how if they break a sweat they're doing it wrong lol. These guys hardly ever get a pump and are big and strong as hell. They are bigger than 99% of the bodybuilder type guys in the gym and they look damn good when they are nearing competition and have dropped their bodyfat down abit.