I bought some cheap and very cheese-grade metric taps and dies in a set. In short, they're about par for the source.
Should a die fit over a tap of the same spec ?
I guess they should not fit very far together before binding, because a die cuts an external thread and the tap cuts an internal thread which have to match with some tolerance for movement.
Also both cutters should be hardened steel, so are brittle and will break before cutting each other. I'm not sure if the tap or the die would break first, but one will go.