I might be completely wrong but aren't the first seconds of a cold MV (MB) start also a sort of mercury starvation? The mercury covers the glass tube at that time.
I know that its pink colour is due to the coating but what would be a colour of a mercury starved fluorescent if the phosphor was scraped out?
Not at all.
The pink color of the MV come from different reason than the starved fluorescents: In fluorescents the phosphor respond with the full spectrum on just the short wave UV. But that get blocked in the MV by the quartz, outer bulb atmosphere and mainly selfabsorbtion in the mercury.
With the MV the phosphor is actually designed to glow pink, because unlike the fluorescent, the (fully warmed up) MV gives out high power in the visible MV lines, which need the pink glow from the phosphor to complete the desired white light. And as the mercury at lower pressure does not emit as much of the visible lines, starting up lamp appear pink.
And even when accepting the mind game and judging what happens there ridiculously according to what should happen in a low pressure fluorescent. And even regardless, how you define the "starved":
"Not enough mercury for normal operation": It means after warmup, so when stable. As it is just starting to warm up, with this definition it could not be starved.
"not enough Hg for a low pressure discharge": With that definition it would be rather "argon poisoned" (too much Ar for a proper low pressure Hg discharge). And heavily "overloaded", so the mercury plasma get selfabsorbing for the UV.