No, mini-split controllers, and any other controllers primarily intended for variable capacity heat pumps and air conditioners cannot earn the ENERGY STAR. This is implied in Version 1; in Version 2 these controllers will be explicitly out of scope.
In the Version 1 test method, at the beginning of the sampling process, thermostats known to be controlling variable capacity heat pumps are eliminated from the population. Therefore, any member of the product family that controls primarily variable capacity heating will have virtually no installations in the sample. Thus, it is not acceptable for them to be considered part of the product family. As a separate product family they would not be expected to have enough installations to analyze properly.