With a boost driver it's not only the IC that has to cope, but the inductor as well.
If the inductor is designed to be physically small it can be under spec to boost from a lower voltage, even if the driver chip has no probem with that voltage per se.
With a fixed frequency driver you'd get to a point of magnetic saturation of the inductor, causing a big loss of efficiency and a driver just unable to supply the set current.
This is not typically dangerous for your laser though. It may run at lower power, it may flicker, but if the driver design is half decent it will not run your laser (diode) at higher power/current then intended.
This is all presuming the driver actually is a boost driver, which it may not be.
When using 2 cells in series their output voltage would often be higher (6 to 7.4 volts) that what the diode actually needs (5.5 to 6 volts), and a buck or low-drop linear driver may work better. Make sure what kind of driver is in your laser!
With blue or violet lasers running from a single cell you can be confident it is a boost driver, but with 2 cells it could as well be buck or linear really.
These SOKY sellers don't seem that tech savvy at all - they specify a duty cycle of 10 minutes on and then 10 seconds off for the 1 watt model. They should realize that this is nonsense, it's only 1.5 percent lower than continous operation, and anyone that ever did any electronics design would have turned down the power by 2 percent just to guarantee you can leave it running continously at that point.
I don't think much work as gone into their maths though, the 2 watt model can be ran at 3 minutes on and 20 seconds off - effectively 90% duty cycle - according to their specs. Since it's exactly the same case i'd call BS here: either you can run all of them continously or all of them will overheat if you try. Considering the size of the things i hope the first one is true, but i will not make any guarantees to that
