The fuel accumulator holds pressure in the CIS injection system after
the engine is shut off to permit restarting during the several hours
until it is again cool enough for the starting injector to come on to
assist starting. A bad accumulator will make a hot engine crank and
crank before sputtering to life, almost like starting a flooded engine.
The hot engine will usually restart fine if restarted within a few
minutes or so, then not want to start without extended cranking until
left to cool for several hours.
The cold start injector sprays additional fuel for cold starts to
enrichen the mixture, serving like a carburetor's choke.
I fought a bad fuel accumulator in my 1974 Porsche 911 several years
ago. When hot it would crank and crank and often backfire when it
started. On a 911 a bad fuel accumulator will often leak wet gasoline
under it. Not sure on a Mercedes.