Should graduate study be done when you are not fully interested in the subject matter?
An unmotivated graduate student will usually be a lackluster student at best. These students will be more likely to be distracted by whatever their true interests are. 

Moreover, in a program like the one you are describing, you will be making a very significant career detour. You would be advised not to make such a move unless you are absolutely sure that it's something you'll want to do for the next four years, since you will have a payback requirement. If you're not sure about it, this is the kind of move that can wreak havoc on your career—particularly if you (re-)discover your dissatisfaction after the classwork is complete, and the service period begins.