Not below their factory defined minimum. Which is all over of place, except for Dell and HP, which around 40 nits minimal brightness.
The ones that don't have more expensive electronics driving the backlight. Eizo's FlexScan EV series is one example.
I have a FlexScan EV, and I don't find being able to turn the brightness down to 1 or 2 nits without any flicker as useful as I thought I would. Even in complete darkness, it is hard to read the screen when the brightness is that low.