EDIT: The information in red is incorrect.
No. It won't work. The T/C head starts out in the fully compressed position. As you tap, you keep the feedrate slower than it should be. This causes the head to extend as the threads are cut.
I have a very nice drag engraver made by a fellow forum member. At the time, it made more sense to buy his than to make my own. But you could easily make one to use. Details here.