At least you didn't do the bone-head thing that I did! We went to South Carolina in March for a week. I did not run Pink Stuff on our return home, (couldn't find any), but did blow the lines out. I had the water heater on by-pass.
In late April we went out again for a 3 day week-end. I forget about the by-pass since I blew lines out and did not have to flush the pink. I flipped on the electric, and after a while, only cold water.
I thought something might be wrong, so flipped on the gas. A few hours later, no hot water.
Then I realied... THE BY-PASS!
I filled the tank with water and expect no electric, element burned out for sure. But was diappointed when ZIP happened with gas.
And the bath house at the camp ground was under renovation (closed). Arr.
Anyway, long story short, took it in for repair. Electric element burned out and the thermostat shot! Got both fixed and been happy camping ever since.
To answer your question ... as stated above, your electric element should have burned out within a few seconds, not allowing the tank to get hot enough to do any damage. (Gas on the other had will continue to heat, even without water .... so I learned).
So if your plug is leaking, its not a big deal. Replace it. Simple solution.