Edit My post has confused me now. Can someone please confirm is jacksnap is right. It would mean my original thinking is good and my later later confused thinking is wrong.
I think jacksnap is correct. I have seen the following experiment. Get two identical springs. Compress one and tie it up with string, and attach one end of a copper wire to each spring. Put both in a mild sulfuric acid solution (maybe 1N). Is the action of the acid on the two springs different (bubbles, etc.). Why?
Yes, the compressed spring has more energy. But it is unlike a battery, because no charge transfer is required. The extra energy is in the displacement of individual atoms from their minimum energy state (mechanical stress). In terms of mass of the spring; the extra stored energy has to increase the mass of the spring by a minscule amount.