Not the healthiest, no. Although some of us aren't very healthy. My BFF turned to me the first time we saw Sherlock and said, "OMG... he's you!!" LOL
I think Mycroft is an ISTJ with a very well developed Ne. He can't foresee people's actions and plan for them like a Ni-user would, so he is frequently caught off guard -- Moriarty plays him, Irene plays him, and Sherlock plays him. An INTJ would have contingency plans in place and some idea of where their actions were headed (think of Khan in the new Star Trek movie -- Ni-dom. Foresees everything, plans for everything, only is undermined because he didn't know Spock could consult with Spock Prime). He also shows Si in everything he does -- maintaining the British empire and proper way of doing things, reminding Sherlock of childhood incidents and what was learned from them, etc.
I also think Sherlock is an ISTP/INTP hybrid. He's very energetic, likes to do hands on experimentation, and notices the smallest details in his environment one moment (Se) and is incredibly lazy, intellectually stimulated, and excited about new ideas (Ne) the next. Not a straight up INTP, but more consistently ISTP (Se -- observe details, Ni -- intuitive leaps / narrow down the possibilities to one conclusion) a lot of the time.