Can a Tesla coil's secondary wiring overlap?
A Tesla coil is NOT a transformer. It is a resonant structure that transfers energy via an coupled resonance. Thinking of it as a transformer is incorrect. 

So the answer to it being OK to have overlapped windings is no, due to the added capacitance of the overlapping windings and capacitive coupling. A Tesla coil is better described as a quarter wavelength helical resonator. It needs a high Q factor and the capacitive coupling of overlapping windings will dampen the resonance resulting in sub par performance.

Update (2 years later I got around to it...):
I should make a diagram someday, while not technically 100% accurate, here is a good analogy. Think of a tesla coil as a long wire that reflects waves at the top end back down. When in resonance, every time the energy packet reaches the base after reflecting back from the top, a new amount of energy is added to the packet making it grow, and again sending it up the coil. 

If you have over lapping wires, as the energy wave travels through the wire some of it is lost via capacitive coupling to other winding layers, and those packets of lost energy continue on, but now  out of phase, their reflection will not line up with the rest of the main energy packet. This will dampen the resonance via destructive interference etc.

You will get a loss of Q not only from over lapping windings, but also if the base material of the tube supporting the wire is lossy at RF, it will capacitivly couple energy out of the coil. In some of my work I have found similar coils (dimensional and wire length etc.) with cardboard vs. polypropylene tubes for the main body can have Q's of 25 vs 175. That means the plastic tubed coil had an additional voltage gain of 7x, and it was very noticeable.