Well, yes and no.
Yes, in that both .380 Auto and 9mm Luger have a nominal bore diameter of .355, which is the same as .38 Special and .357 Magnum.
No, in that .38 Special has not been chambered in an autoloader. There are two .357 Magnum autoloaders that I know of, the Desert Eagle and the Coonan series of 1911-a-likes, and they would be able to chamber and fire .38 Special, though not cycle the action (not enough kick - the Desert Eagle doesn't cycle except with moderate-to-hot .357 loads).
9mm Luger ballistics are roughly equivalent to .38 Special (and I do mean *roughly*), so performance wise you'd have a match, but you would not find an autoloader that would chamber the same .38 ammunition as a revolver.
Of course, there's the Medusa multi-caliber revolver, which will fire just about any straight-walled pistol cartridge with a .355 bore diameter known to man, but that's another can of worms entirely, and probably the opposite of what you're looking for.
Hope this helps.