If I used a pulse start metal halide or a high pressure sodium ignitor to start a fluorescent tube, will the 3.5-5.0kV pulses from the ignitor instantly destroy the lamp's cathodes or will the fluorescent tube merely instant start with intact cathodes?

The cathodes of fluorescent lamps, aren't intended to get 1-5KV. These ignitors will short the lamp life.
Fluorescent lamps should start with hot cathodes.

I wouldn't even attempt to try this!

I might be an interesting way of finishing off EOL fluorescent tubes!!!!

Should instant-start even without the ignitor.
I'd stand well back (and do it outside) if messing with a fluorescent on a HID ballast.
 (probably be nice 'show' to fry a spent tube that way though .lol.)

Should instant-start even without the ignitor.
I'd stand well back (and do it outside) if messing with a fluorescent on a HID ballast.
 (probably be nice 'show' to fry a spent tube that way though .lol.)

In some cases, me, funkybulb, and some European members have used HID ballasts as preheat ballasts for high wattage fluorescent tubes. For example, I have gotten a European specification F58T8 fluorescent tube to run slightly below its rated current, but decently well on a North American 50w M110 pulse start metal halide core and coil ballast. In that setup, I made sure to remove the ignitor and use a Philips S10 fluorescent starter instead to start and run the lamp like it would on a preheat circuit that it is normally designed for. Even though I was able to get the tubes to run on these HID ballasts reasonably well, I still do not recommend any inexperienced members to run fluorescent tubes on HID ballasts unless they consult with members who are experienced with conducting lighting experiments and know how to do them properly.

If I used a pulse start metal halide or a high pressure sodium ignitor to start a fluorescent tube, will the 3.5-5.0kV pulses from the ignitor instantly destroy the lamp's cathodes or will the fluorescent tube merely instant start with intact cathodes?

Assume the idea is to use just a (presumably superimposed) ignitor on a standard fluorescent ballast.

Short time it wont damage anything. The "xxxkV" on the ignitor is the voltage the ignitor is able to reach open circuit, without any breakdown happening.
The real voltage is always clamped by the discharge, so if the fluorescent ignites at 800V peak, there never will be anything more than that 800V, the same as with e.g. 700Vrms (so 1kV peak) OCV instant start ballast.
For the cathode damage is important the peak current, not the open circuit voltage the ignitor may achieve. Because the initial gas breakdown, so what these HPS/MH ignitors are designed for, does not need any current at all, the ignitors are designed to deliver only very small current, way below what even the smallest fluorescent can handle.
The only extra wear with such form ballast would be the same as with any other cold cathode starting (instant start) ballast.

But the problem is, the lamp would usually just not start.
The thing is, the starting sequence for cold cathode starting has 3 phases:
1) Ionize the gas. Needs no significant current, takes few us, but needs high voltage, so a narrow low current HV pulse is enough for that.
2) Heat up the electrodes. For that you need to pass high enough current for long enough time, so the cathode ion bombardment releases enough heat to warm it up to emission temperature. Takes some 100's ms till some second or so. Because the gas is ionized, you don't need really a high voltage, but because cathodes are cold, you need about 100V extra to extract electrons from the cold cathodes to maintain the arc. With MH or HPS this happens when the arctube is cold, so the anode column has nearly no voltage drop, so the ballast OCV is able to feed this state. But with low pressure discharges (fluorescent, but also the LPS) the anode column has nearly the same drop as normal burn, so it requires the ballast to deliver higher OCV. Because the extra has to actually heat up the electrodes, it means it has to deliver sufficient power. When the ballast OCV is not enough, the HV ignitor has by far not enough power for that, so the lamp won't start.
3) Stabilize arc power. That is normal lamp warmup and burn. Here the electrodes are at full emission temperature, the cathode fall is low, so the high pressure lamp will have the low arc voltage when still cold, the low pressure lamps have practically their final arc voltage drop.

So when you use an MH/HPS ignitor to cold start the fluorescent, it may get stuck in the 1'st stage (the ignitor just causing gas breakdown), but no significant current will flow in the 2'nd stage. So the lamp will effectively glow with cold electrodes at rather low current, so over longer time the cathodes will get destroyed by that low current cold cathode operation, the same way as when the lamps would be operated on e.g. NST (very low current drive). It won't matter if the low current comes from an igniter or from any other low current source.

The situation will be different, if you will be using LPS ignitor. These are explicietly designed to deliver sufficient HF current in the 2'nd stage (the cold cathode glow mode) to warm up the electrodes quickly.

Other use of the HV pulse ignitor would be to ignite the lamp when the electrodes are heated separately (a kind of RS ballast) but the ballast OCV is not enough to breakdown the gas. Because the electrodes are already warmed up, the HV pulse gas breakdown will cause immediate transition to the 3'rd stage (hot cathode discharge), so normal burn. But for that the insulation of the filament winding would have to be strong enough to withstand the full unclamped ignition pulse voltage the ignitor is able to deliver in case the lamp is missing or defective (e.g. lost vacuum,...), so a faulty lamp wont cause ballast destruction.