I'm being curious here. If an electronic ballast made for the UK electrical system (Philips Dynavision / Primavision for eg) is rated for 220 / 240V, 50/60Hz; or 208 - 277V 50 / 60Hz; and works on the UK single Phase 240V system, would it stand the North American 240V 2-phase live (120v on both live and neutral) or would that kill it?

If the voltage stays within the limits, there is no reason for it to not work normally.
Speaking about normal ballasts, not about some emergency function or so that somehow analuyzes the mains and happens to use the frequency being off as a trigger for something. Normal electronic ballasts don't care.