In the opinion of the assembled brains trust, If I used neon
flicker candle lamps with a normal everyday light dimmer,
will they strike OK if the level is brought up from minimum,
and will they unstrike (!) if the level is reduced back to minimum?

The minimum level is (I assume) zero, so... no, they'll shut off.

As the strike voltage is higher than the sustain voltage, you should be able
to turn down the dimmer a bit. However, I suspect the lamps won't get
dimmer -- rather, less of the flame area will be illuminated.