it's quite the opposite, high speed require more current therefore more resistance and less voltage.
the more "power" your miner "takes" the more drop in voltage you get
in more details.
assuming your voltage reading "unloaded" 240v.
if your miner needs more power , it asks for more current from the source (volt) , the more current that moves thought the wires, the more heat it generates, the more heat the more the resistance, the higher the resistance the less the volt.
so your miner needs 5 amps 240v might drop to only 239.
but if it needs 7 amps 240v might drop to 238.
if it needs only 1amp it might stay at 240.
all the above numbers are nothing even close to reality, but just an explanation, you could have your miner at full load and it may still fail to generate enough resistance that is capable of dropping the voltage by anything measurable.
The gear says 200-240. So if 243 kills them. What would 195 do?
low voltage can damage your PSU , the psu has an ideal rated power of Volts * Amps it needs to keep it at x value
if the voltage drops it will try to cover up by drawing more amps (current) , and as explained above this will cause more heat , most of the times more heat than what your PSU can handle and that = psu damage.
but usually those psu come with voltage protection, which indeed is not perfect, but i am pretty certain it can handle at small drops and spikes.