Some devices, like switch mode power supplies, require a minimum load across the output. If the minimum load is not met the internal components tend to fry. Try running a small current consuming device on an old computer power supply and it will eventually die.
I've never seen a driver board for >10A motors, but if one was designed to operate at a minimum of 10A I would suspect the designers added that requirement for a reason. I'm sure it would work....for a little while.