Absolutely not. As long as air is lighter than water, air will rise to the top of the system, which is the header tank. If that wasn't the case, then the funnel wouldn't work at all.

There is no "atmospheric side" of an automotive cooling system. When operating, everything is pressurized.

These wacky procedures are completely unnecessary. Air bleed would be served as well by slaughtering a chicken and making a burnt offering of the entrails.

I'm surprised to hear that Mercedes relocated the thermostat to the top on the W210 diesels (they certainly didn't for the gassers, and it's their style to stubbornly cling to a design until it's flogged into submission). If this is the case, then the proper thermostat will either have a bobble valve or a weep hole to allow air to rise out. Again, there should be no need for incantations.