Yes - but follow the steps in the manual:
From the manual:
Before driving into a car wash In order to ensure that the vehicle can roll in a car wash, take the following steps:
1. Drive into the car wash.
2. Engage selector lever position N.
3. Remove foot from brake pedal.
4. Press the Start/Stop button.
In this way, operating readiness remains switched on, and a Check-Control message is displayed.
To activate drive readiness:
1. Depress the brake pedal.
2. Press the Start/Stop button.
Pressing the Start/Stop button without stepping on the brake turns operating readiness off.
Also, check out the car wash operation/mechanicals ahead of time - some have reported getting their roof antenna knocked off in particular car washes.