With the limitation that you will probably have to keep the heaters running, at least at low power, I would guess you might be able to dim down to about 50% before flicker and flashing become too obvious. It certainly isn't recommended though and it certainly won't work if you 'PWM' the incoming AC to the ballast unit, you would have to do it directly to the tube itself.
You have to understand how tubes work, they are not like conventional filament lamps where the brightness is related to the power you feed them. They are more like an arc lamp, you have to go over ignition voltage to start them and then control the current through them. A standard tube will not light up if you just apply a voltage across it, they need assistance from heated electrodes at each end and a high voltage kick to ignite them. If the voltage drops below sustainable level, you have to repeat the process to make them light again. When they are lit, the tube conducts heavily and becomes almost a short circuit across it end to end, thats why the ballast unit is needed, it limits the current to a safe level. When you use PWM you hit two problems, the first is it is a square wave which is unipolar, you have to convert it to AC, the second is you have to produce the PWM at low frequency so the ballast can work and synchronize it to the mains AC waveform.
Try a simple experiment: A standard triac light dimmer, the kind you fit to a wall instead of a switch, uses phase control which in this case is almost identical to PWM. Wire one in series with your lamp and see what happens. The control adjusts the firing time of the triac from almost zero to almost 100% and it does it at mains AC frequency so the results should be comparable with a real PWM driver.
Brian.