Oh, that's just an integrated drill/tap. Totally different than what I thought you had.
I thought you had one of these:
The one you have should in theory not present any problem with following the hole since it's also making the hole (though it could easily end up with both being non-perpendicular to the surface). The one above is much more difficult to align perpendicular to the hole since it has almost no lead in and the flutes are more "aggressive" than a standard hand tap.