Not sure how the clutch pedal would affect the differential, but ok...

The center bearing mount does allow the driveshaft to move a bit. It's a rubber "bellows" looking piece to allow some lateral movement. What isn't normal is if the driveshaft just flops around, usually means that the rubber has rotted and the bearing is just flopping around unrestrained.

If you know the popping noise is coming from the rear end, don't forget to check the CV joints on the half shafts. If the boots have failed, or the grease has run out, they can make a heck of a racket when they fail.

__________________
Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]