Yes, you can run down the road with the HW tank empty, just don't forget to fill it before you turn it on.
To me, the larger question is why do you empty it if you're not winterizing it? This last winter, due to winterizing, was the first time our HW tank has been empty since the last time we winterized it three years ago.
Actually the orange Nodwell pictured below in my signature has a 50 gal motoraid HW tank I made myself. Sometimes I run it full of water and other times I don't. Never any damage to it.
Bill