Scan rates of monitors are typically 60Hz and above. Assuming Windows operating system; start>settings>control panel>display>settings
That will tell what the vertical scan frequency is. The reason why flicker is visible when something electromagnetic running off the mains is near the monitor is because the flicker frequency is the difference between the mains frequency and the monitor scan frequency. So, for a 60Hz monitor, the flicker is 10Hz and therefore very annoying. As the electron beam is responsive to a magentic field, it can also be deflected by external fields as well as those intended from the monitor's own scanning coils.
Incidentally, this is one reason why television vertical scanning frequencies are the same as that of the mains, though no longer actually synchronised. It was purposely done to avoid this problem. The other reason was to minimise the effects of imperfect power supply filtering in the TV sets themselves.
Placing a permanent magnet (eg. speaker magent) near the monitor causes the colours to change as the purity is being upset. Instead of each of the R,G & B electron guns being aimed at their R,G & B phosphors on the screen, the electron beams are shifted onto the wrong colour phosphor. This can also happen if the shadow mask becomes magnetised over time in which case it needs to be degaussed.
It is surprising how affected some monitors are; I've seen even small plugpack transformers say 8" away from a monitor cause a problem. If the transformer, fluoro light choke or whatever can't be relocated, changing the orientation can help as the magnetic field from such devices is directional.
Of course, using an LCD monitor eliminates all these problems.
To get back the the question, Kiwi, I'm wondering if you're talking about an optical effect...ie; the actual light from the fluoro tubes causing an effect. The answer is no because the monitor is generating it's own light. If you were using a mains operated fluoro light as a backlight for an LCD screen, then yes you would see a stroboscopic effect. One reason why the fluorescent tubes used for such purposes run at high frequency (~30-100Khz).
