Hi, yes you can use Dexron III, but that is not the most recommended ATF oil.
The most recomended ATF oil for the NAG 722.6 is a MB 236.14 specified ATF oil.
Please take a look a the MB specification 231.1:
http://bevo.mercedes-benz.com/d/d/en/Spec_231_1.pdf
I've used Fuchs Titan ATF 4134 for my last ATF oil change. That is very good, because gear changes are very smooth now.
Don't know if this brand is available in the U.S.
These are the recommended ATF oils by Mercedes Benz for the NAG 722.6 with the MB 236.14 specification:
http://bevo.mercedes-benz.com/bevolisten/236.14_en.html
Regards
Markus