How common is it to switch to a tenure-track position from a non-tenure-track position in the same institution?
Like many things in academia, the answer will likely depend upon the institution.  In most, I would think that a non-tenure-track and a tenure-track position are actually different positions.  You aren't just changing a title, but you are leaving one job and starting another (at the same institution). I would imagine that most do not have official rules about the number of times you can change jobs, although there may be unofficial scuttlebutt to the contrary.  This should be outlined in the faculty handbook/guide.


  Is it ever a good idea to ask when interviewing for a non-tenure-track position whether there is a possibility of switching to a tenure-track position down the road or what the institution's policy is surrounding switching tracks?


If you are interested in a tenure-track position, I think this is a very important question to be asking, and is not viewed negatively by any reasonable person. The chair or hiring committee should be able to let you know about this possibility.