The car was parked and idling in the video, so yes.

I'm going out of town tomorrow and won't return until Monday. I'll try to take the belt off and try to isolate the cause then.

Coolant Pulley play...
W202 coolant pulley play - YouTube

I took the belt off and checked the tensioner. It spins with a ticking noise... not sure if that's normal. I also checked the coolant pulley for play, and as you can see in the above video, there is some play that causes a knocking sound identical to the video with the engine running. Replacing water pump should do it? Or should I replace the tensioner while I'm at it as well?

Tensioner video:
Nov 19, 2013 - YouTube

Thanks guys!