Sure... smaller diameter equates directly to reduced current carrying capacity. Not so much due to resistance, but more so because high currents generate heat. Each wire size has an upper limit before the metal melts. Then all hell breaks loose. I am sure that your wires would have a reduced capacity due to the stretch effects as well as the reduced diameter. In other words, if you draw it down to a 20Ga size, it will likely NOT carry the same current that a 20Ga wire would. Well, it would be "hotter" at any given current than the equivalent sized un-stretched wire.
I reference to bends and the like where there is no (very little) deformation pressure. In stretching, I think that it is unavoidable. The stretch would have to be over a period of hours to keep the lattice from hardening, and not even likely then.