Basic question seeks simple answer.

[ZiNgA BuRgA]

You don't have to use MyBB's template system at all actually.

If you're trying to integrate scripts together, it will really depend on what level of integration you want, and how the other scripts function.  For example, if all you want is the MyBB header on the other script, you'll need to somehow pass the $header variable to the other script, depending on how it outputs HTML.
So unfortunately, I can't give you a simple answer to that.