When building a Tesla coil, is it possible to use the primary and secondary coils of a second transformer in place of the usual coils?
From this website entitled Stefan's Tesla coil pages: -


  Typical coupling coefficient for standard Tesla coils are in the range
  between 0.05 and 0.2. The looser the coupling, the shorter the sparks.
  But if the coupling is too tight, there will be racing sparks along the
  secondary and breakdown between the primary and the secondary.


See also pretty much the result of any search on the subject: -



So, if you are unsure about what I'm saying go google some stuff. A regular transformer (be it for a neon sign or for use in a microwave oven) will have a coupling factor of nearly 1.

You need a loose coupling factor so that the individual coils (primary and secondary) can be resonant tuned. It's the resonant tuning that creates a monstrous voltage magnification and not necessarily the turns ratio although more turns on the secondary will produce more voltage.