I do it quite a bit, but i also compete in strongman, so its essential. For a bodybuilder, I would do cleans by them selves and push presses by themselves. I would not do them together though. You'll either fail on the clean or on the press and I feel its better to work on them seperately. Cleans are great for traps, push press for delts
The clean or power clean is a good exercise. But not a main stay of body building. Heavy deadlifts are preferred over cleans. More chance of injury with cleans due to the explosive nature of the movement especially if some serious poundage is involved. The push press or press portion of the clean and press is also a great exercise for building strength. but again not a main stay of body building. Dumbell presses, seated presses where your back is supported are preferred for building muscle. If as B-rad stated you are doing stronman work then the clean and press, power cleans and push presses are a must. But for building mass as a body builder, well let's just say there are better exercises for this.
i used to do it regularly back in 1998 thru 2004, i got alot of trap and shoulder development from it, it also was responsible for a few strains on forearms and shoulders. but the reason i stop doing clean and presses was the over development of traps.
It's really more suited for a power or explosive athlete. It can be beneficial in a bodybuilding training regimen if used at the right times, but personally I feel like it's more important for other types of athletes like olympic lifters, power athletes, strongmen, fighters, etc.
Builds coordination, explosive power and core strength. It's great for learning hip drive.
If it makes you feel better you can think of it as speed work for the deadlift.
It's my belief that putting 50-100 pounds on your deadlift in a couple of months generally results in muscle growth. This exercise alone is responsible for pushing me from the mid-4's to the low 5's. ( Deficit deads got me from low 4's to mid 4's. )
I suppose if you are already a pro/near pro and are pushing enough weight to put on serious mass then it's probably not all that useful. Assuminng anyone who is already advanced/elite has developed the skills to move heavy weight.
In my case it's helping push my deadlift into the 2.5xbodyweight range and I'm pretty sure that this will translate into new muscle.
The assumption underlying all of this is that you need to develop an adequate level of strength in order to develop an adequate level of muscle.