Effect of lower voltage supply in flash circuits
There is no standard stating how a manufacturer must or should implement a flash charging system.

However, my experience from many years of using many camera flashes of a wide range of energy outputs, and with a wide range of AA cells, rechargeable and primary, is that in all cases 


The flash will not fire until the internal "reservoir capacitor" is at a certain level (shown by a "ready" indicator lighting).
Lower capability batteries increase the time taken to reach this level (as you'd expect), and that
Flash brightness is independent of the battery state EXCEPT in full manual mode - see below. 
Use of lower voltage cells with high discharge current capability will often result in faster recycle times than higher voltage cells with lower discharge capacity. For example, a good NiMH 3000 mA cell will provide up to about 10A when fully charged, falling to a few amps towards the end of its capacity. Primary cells vary with type and brand. A good AA Alkaline cell may approach a good NimH cell initially but fade more quickly. A modern camera will utilise the battery available discharge rate over a range of battery voltages. eg typically from about 4V to 7V+ for AA cells. 


When carrying out extremely flash-intensive high shooting rate photography (eg on stage dancers or similar) I usually choose Alkaline cells and discard them when the recycle time becomes excessive. This is usually in &lt;= 100 flashes - depending on ambient light and distance to subject which affects energy use. I use Alkalines cells NOT due to their energy capacity but because NimH or Alkalines come out of the flash at well over 60 degrees c in those circumstances. Alkalines can be discarded in a safe place 'on the spot' rather than having to juggle 4 'red hot' NimH cells. 



All properly engineered flashes use the energy required to implement the desired exposure and, if there is charge remaining, terminate the flash cycle and retain surplus energy for subsequent use. This allows either a single flash that consumes all available energy (eg manual 100%) or multiple lower energy flashes if the system so dictates. 

A flash will often continue to top up the internal capacitor above a certain minimum level once the "ready" indicator illuminates. This allows multiple flashes of less than 100% energy.



Specifically:


  Does it mean less maximum light emitted by the flash?


No.
It results in longer time to recycle.


  I'd say that lower voltage mean lower maximum light emitted by the flash, but same recycle time (since the time constant depends only on the capacitance and the resistance).


Not in any example that I have ever seen over many years EXCEPT when the flash is set to Manual mode and all available energy is expended by the user as soon as the flash allows. In those cases only, a higher recycle rate at lower intensities is possible. Most modern flashes, apart from very low cost ones, have one or more automatic modes as well as manual mode, and most users use the flash in automatic mode almost always.