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.

Some people do further study because they are interested, indeed passionate about the topic matter. Others do it to improve their job prospects/career outlook/ultimate pay packet.

Ask yourself which category you fall into. If you are not interested, then you may not enjoy it and may not succeed unless your motivation is more financial.