If the tank should run dry, and it is still turned on, yes, you have a good chance of burning out the tank. Shut the electric or gas to tank off. No reason to be heating water for 3 weeks while you are gone. Then, let it trickle, if you want. When you come back home, and turn the water on, and the tank fills up again, then restart the tank to heat the water. I assume you are still going to be heating the house for those 3 weeks and having someone check it every couple of days, to make sure there are no problems? Since you are shutting the main water line off, there may not be enough pressure in the tank, to even let it drip.

Why howdy greywinds,been so long since I saw you post I begin to wonder if you were ok.

Let's take this this from the top in bite size portions. When you say " I plan to turn off the water at the main inside valve. "I take it that water first enter's home in the basement. If water is turned off inside building BEFORE it is above ground,that is good. Once main water valve has been turned off there will be no pressure to drip hot water but that's not necessary anyhow. If water heater is gas,it has a vacation setting on temperature adjustment. Set it to vacation to save a little gas but it will not harm it to leave it as it is. If water heater is electric,temperature adjustments require removing 2 panels from front of heater,(not recommended for average homeowner). You can trip water heater breaker to save $5 worth electric or leave as is without worry. If you were gone more than 60-90 days it would be necessary to adjust temperature to prevent boiling water low in tank. There's benefit to leaving temperature at normal. It prevent's alge growth an stinky water that must be flushed out on return. Now let's talk about the line through attic. In the past,if it only stopped water flow until it thawed,it will be far less likely to freeze when now pressure is in it. Water always run's downhill so the pipe in attic will drain dry when pressure is turned off at main and all faucets opened. Leave most if not all hot and cold faucets open during vacation. For best defense in case of fire, all rooms should have doors closed to slow spread. For best freeze protection,doors to baths,laundry,bar,kitchen or any place with plumbing should be left open to alow warm air to circulate. Injoy vacation. Questions?

Thank you both for your insights. When I did google searches on this subject, the prevailing wisdom was to not shut off the water tank or even turn it down, citing bacteria growth (in line with Klem's comment). It's an old heater and I feel that the less I mess with it, the better.

Klem, can you clarify this sentence:

Now let's talk about the line through attic. In the past,if it only stopped water flow until it thawed,it will be far less likely to freeze when now pressure is in it.

Did you mean to write when now pressure is not in it?

"Did you mean to write when now pressure is not in it?"

I should have said,the pipe is less likly to burst if (A) there's no pressure in pipe (B) pipe has been drained leaving air pockets in pipe.

To accomplish this you must open ALL faucets after main has been turned off. That alow's water in pipes above level of faucets to run out of pipe.

OK, got it. Thanks!

Not to get the cart before the horse,but I should mention something that often happen's after water has been off several days. The drain on water heater tank sometimes drips for a day or two. Set a pan beneath drain for a couple of days after pressure is restored. If drip continue's past 3 days,the washer/seal is replaceable same as an outdoor hydrant. No need to replace heater over a 25 cent washer.