You won't see any significant strobe effect anyway.
The decay time of the phosphor is much longer than the exciting voltage frequency.
It does not have time to extinguish before the next half cycle.
If you switch off a tube in darkness, there will often be a bit of ghostly light from the tube for several seconds.
You can see vague sort of strobe effect at certain chuck speeds, but it's pretty obvious it's still rotating.
In industrial applications alternate banks of fluorescents can be run from different phases to reduce the effect.
Some tubes can be run from DC IIRC, but it causes polarisation, and the tube life is geatly reduced unless they are turned end to end often. Not going to happen is it?

My old ML7/T was used for about 15 yrs with a twin 2 foot above it.
Never tempted to poke the chuck, when it was whizzing round it looked like it was whizzing round.
BC