Yes (note: as it comes to real details, I have not yet used a GD). Depending on the driver, there could be damage if it needs to push out more than 5.4V, or if you hook it up to higher than 5.4V input.
I wouldn't say it will take what it needs, as much as say it will take what it can get. But, what it wants to take (Amperes) does not match up perfectly with what you can measure to give it (Voltage).
LEDs do not have Vf all that close to each other, even in the same batch. One may push out 100 lumens at 3.6V, one may need 3.8V. But, they will be much closer together when it comes to current. One at 1000ma will put about the same amount out as another of the same bin at 1000ma. If you just run them by voltage, the outputs will be wildly different.