I'm not certain on how long your E320 takes to "wake up" but I noticed that my 98 E320 does not respond to a wide open throttle response (gas peddle to the floor) during the first 5 minutes of a cold start. The engine has a few second delay before the engine starts to rev up.
Since I don't normally require a wide open throttle response expecially before the car warms up, this does not present a problem for me.
Although my 98 E320 has the V6 engine with throttle by wire system I thought I would share the experience that I encounter from a cold start.
1998 Mercedes E320, 200K Miles
2001 Acura 3.2TL, 178K Miles
1992 Chevy Astro, 205K Miles