Yes it's possible and it actually works rather better than with high pressure mercury. The reignition voltage peaks on each half-cycle are lower for HPS lamps than HPM so it is easier to run on a resistive ballast. It is especially good with standard xenon-filled HPS lamps. With the neon-filled types (penning-start, which also self-ignite with a tungsten ballast) the thermal losses from the arc are much higher, due to the increased thermal conductivity of neon vs xenon, and those do then show more problems on a resistive ballast. But are easier to start!
are you sure about that James? I hope you dont mind me saying but it sounds like you have got that back to front, AFAIK mercury lamps have a lower re-ignition voltage then HPS lamps, and this in itself is why no one ever commercialised a self-ballasted HPS lamp
certainly in my own experience with a oscilloscope, on standard magnetic ballasts, I note that a HPS lamp will have distinctive re-ignition peak, compared to a much smoother waveform of a Mercury lamp
and many years ago when I tried to incandescent ballast a HPS lamp in the past (a 35W SON-E 85V Sylvania HPS lamp in series with a 220V 200W GLS lamp), it always lead to the HPS lamp extinguishing, since the resistive ballast lacked the phase shift that keeps a HPS lamp going on a magnetic ballast