The higher the voltage, the higher the current
You are correct, in a sense. Current is directly proportional to the voltage and inversely proportional to the resistance. So, an increase in the voltage will increase the current as long as the resistance is held constant. So by increasing the potential of your power source, while not increasing the resistance...then that can certainly blow a coil.
In terms of the question from the OP... Heating your atty coil for long periods without cooling from e-liquid (dry burning) will certainly damage it faster....if not flat out blow it. However, taking 8-10 second drags while the coil has e-liquid cooling it will probably not cause it to fail much faster than it would if you were taking 5-6 second drags. Basically saying... Keep it wet.