No, it is not. You will destroy the starting electrode and cause lamp failure. Take out the ignitor before putting the lamp on the ballast.
Actually this is not correct. There is no risk for the probe itself.
In fact if the MV lamp would be ignited only when cold, nothing will happen at all.
But that does not mean it is safe to run MV on a HV pulse start ballast, on the contrary, it is far more dangerous than just a starting probe failure would be.
When the lamp is cold, the breakdown voltage within the arctube is low, so it will just short out any higher voltage (the igniter is designed for exactly that to happen, so the igniter is safe), so no harm to anything.
But the problem arises when the arc extinguishes and the igniter starts to trigger.
The main problem is, the connection and metal structures arrangement and the eventual gas fill (or its lack of, ie if vacuum is used there) is designed so it withstand the voltages it is expected to be there, so no breakdown or discharge would ever happen there.
With HV pulse start lamps the lamp design counts on the presence of the high voltage of the ignitors (large distances, ionization suppression components in the outer gas mix or the use of hard vacuum,...). The consequence is, the outer fill can not be made as optimal for thermal management or phosphor chemical stabilization and e.g. the lamp is not as mevhanically rugged as it could be without these limitation (or needs higher assemble complexity so cost).
On the contrary because MVs are designed to be started without the HV pulses, the outer assembly and fill don't need to withstand that high voltage, so are more optimized towards lamp performance and ruggedness (and lower cost). Of course, when you expose such design to a HV from an ignitor under a condition where the arc tube wont restrict the voltage (because it is still hot so pressurized), the HV pulse may cause breakdown in the outer and so ignite an arc there.
Now unlike the arctube, the outer is not designed to handle the arc at all, so it will within a few second destroy the outer and even very likely cause the outer to explode and shatter the glowing red remains all around.
Obviously that is quite potent to cause quite severe injury directly, but as well as set the surrounding on fire.
So it is not because the probe, butbecause the lamp design as whole (mainly around the lead wire seals in the outer bulb) does not tolerate the high voltage. Ironically typical probe assembly would be able tohandle the high voltage well.
And the same danger is with MV retrofit HPS lamps, many used just penning mixture buffer to ignite at the ~230V OCV of an MV ballast. These may get destroyed by the HV ignitor the same way as MVs, even when they have no starting probe at all.
