This is a hotly debated topic and no one really knows the answer from a scientific standpoint.
So I look at it like this ...
PUMPS DO HELP YOU BUILD MUSCLE through motivating the individual psychologically.
To understand this - you need to go back to the bible of bodybuilding, the Holy Grail of muscle building.
Yes, that's right - I'm talking about the movie ... PUMPING IRON!
In that movie, Arnold talks about "getting pumped" and what a "great feeling" it is. He talks about his skin feeling so stretched ... as if his muscles were about to rip through his skin. You can tell in eyes that Arnold really "gets off" on this feeling.
So if you lift and get pumped - and groove on looking at yourself in the mirror after a hard set - and if you like what it visibly did to your physique - you are more than likely going to come back for another round of lifting the next day.
I will tell you flat out - I've been working out in gyms for 30 years and sometimes it can be tough to motivate yourself to get in there and lift - and put all you have into it. Anything that makes you want to go into the gym and go at it is helping you build muscle.
I think gyms have figured this out too. They all have mirrors everywhere in the pump rooms. Yeah, the trainers will tell you they are there so you can watch your "form" ... riiiiiiight. Well, I've been lifting so long I know the proper form for a deadlift in my sleep - I don't need no mirror and I believe that Coach Rippetoe even says don't watch your form for deadlift in a mirror, if I remember correctly.
I'm not watching my form ... I'm thinking ... "ONE!" (Goddam ... look at my ****ing shoulders!) ... "TWO" (**** my anterior heads are bigger than my ****ing head!!) ... "THREE!" (Mother **** ... that chick is checking my ass out behind me!)