Is it safe to charge the battery in place on 2006 SLK? Has anyone done this before successfully, and if so, do I need to take special precautions?

 

Batteries charge whilst the vehicle is being driven, Charging when stationery is little different.
Most modern cars have a battery vent to atmosphere anyway to pipe away explosive (hydrogen) gas. So best in a ventilated area especially with a little draught.

I guess the important bit is not to overcharge but so long as you are using a purpose built charger MY VIEW would be OK.

However I guess the real issue is why you need to charge the battery? Unless you leave the vehicle for extended periods 1mnth + there should be no problem.
Stuart