If the switch at the water heater itself was off, no harm should have been done. And, yes; water heater elements can usually be replaced Instead of replacing the whole water heater.
Where problems occur is when the heating element is on with no water in the tank. Be sure your water heater tank is full of water (temporarily open the overflow valve on the heater until water flows out) and then turn both switches on (control panel and water heater). You should have hot water in an hour or two. If you need it more quickly, activate the propane burner too. You can run them both at the same time.
Just remember that you need water in the water heater tank before using the electric element.
TJ