Yes the two parts need to be separated. Take the opportunity to completely clean the plunger ensuring there is no dirt and it depresses without any sort of binding and center the plate.
I also recommend getting as much dirt and debree out of the intake manifold. When you open the throttle valve attached you'll notice a swamp of horror below. Just soak some of it up as best you can.
Some more info and pics here:
http://w124-zone.com/articles.php?article_id=23
With the fuel distrib removed, check your motor mount on that side...it can be accessed 10x easier with it removed.