I had a thought experiment: Imagine 4 fluorescent tubes, all of them 1200 mm long and 38 mm diameter.
One of them is a standard F40T12 with about 3 torr of argon. Another tube is filled to 25 torr of argon. A third one is only filled to 0.1 torr of argon and a 4th one only has the mercury vapor pressure in it, no gas filling.

If we connect them to a current source supplying exactly 430 mA of current, am I right to  assume that the tube filled at 25 torr would have the highest arc voltage and the one containing only the mercury vapor pressure the lowest?

I assume this effect is not linear, so tripling the gas filling pressure wouldn't triple the arc voltage.

These experimental lamps wouldn't be practical, but it would proably offer the possibility of some interesting experiments.

I couldn't find any documentation about gas filling presures F30T12 and F30T8 (pure Ar in both). Since a reduced tube diameter increases the voltage, it's expected that the gas filling pressure in F30T8 is significantly lower to keep the arc voltage of the two tubes the same.

Another interesting topic would the the gas filling old Philips 16, 32 and 50 W tubes (pure argon despite being T8), which have significantly higher arc voltage than standard 600, 1200 and 1500 mm long tubes.

Increasing inert buffer gas pressure (within a reason) will just slightly increase arc (burning) voltage. What will happen at pressure decrease is more complicated, voltage will certainly increase again at some point. A tube with no buffer gas won't ignite at all at practical conditions.

Wouldn't decreasing the buffer pressure to zero make it into a kind of Cooper-Hewitt lamp? Just with oxide instead of liquid mercury cathode, but the discharge environment otherwise the same.
Yes, these tend to operate at 10x higher currents than fluorescents used to do, leading to a completely different loading, working temperature and mercury pressure.
But CH's were also started by a HV pulse via a (capacitively coupled) external electrode, which should work with the small solid cathode even better than above the flat, smooth mercury pool surface.

Are you sure CH tubes (not the ones which started by tilting) did not contain any buffer gas? Without a buffer gas fill, mercury filled tubes are quite hard to get ionized - see how those 'octopus' mercury rectifiers and ignitrons work.

My wild guess is that at room temperature, fluorescent tube without a buffer will pass some current and even ionize some mercury vapor while filaments will be hot by external preheating, just like the way a regular vacuum diode will work. But will not sustain a discharge by itself until walls are not hot enough for mercury pressure to reach some tens fraction of mmHg, at about ~100C temperature.