kevhsuAutomatic supports gasoline and hybrid cars. If you use Automatic in a diesel car, there won't be any damage to the car or the Link. The reason we say diesels are unsupported is because some of the features of Automatic won't work. In particular, the mpg and gas prices will be completely off.
If you don't care as much about those features, then you can use Automatic in your diesel car. (We definitely have customers using Automatic in diesel cars.) Just keep in mind that we might not be able to help you debug some issues that may arise.
Check out this topic on diesel in our Community: http://community.automatic.com/automatic/topics/what_would_actually_happen_if_i_used_in_non_supported_diesel_car