I don't believe standard electronic flash meters would register correctly, as there is no built-in matching 20 millisecond (1/50 sec) delay before measurements are triggered. That means if the meter is set to, say, 1/125 sec, then that measurement interval would begin at the instant the bulb igniter was lit, and would only capture a small portion of the rising intensity as the bulb burned up to its maximum output.
However, if the meter was set to 1/25 sec, then it might measure the full volume of light on both sides of the peak. This would be the equivalent of an unsynchronized open flash scenario, but would still not mimic the 20 millisecond delay used with mid-range shutter speeds faster than 1/25 sec, where the goal is to synchronize the mid-point of the 1/125 sec shutter interval with the mid-point of the intensity curve of the burning bulb.
The analogous photographic situation would be to set the 'X' sync speed, then use flash bulbs. Anyone (including myself) who has ever switched from electronic flash to flash bulbs and forgotten to switch from 'X' to 'M' knows the end result. The shutter (set to mid-range) opens and closes before the bulb can burn to useful intensity, and the resulting negative looks as if no flash was used at all.
My guess is that a standard flash meter would react in exactly the same way.
Ken