[Jack]

In a 22 autoloader, like a 10/22, you need the power of a long rifle cartridge to cycle the action. If you tried to fire shorts in a 10/22 the action would not eject the empty and load another cartridge into the chamber.
Now, if you wanna single load them, you can put 22 shorts into a 10/22 singly, and fire them, with no harm to the rifle. You'll have to open the bolt by hand to eject the empty. Done it many times.
My 10/22 will feed 22 longs just fine, and cycle them- most of the time (got a box by mistake many years ago).
These days, if you find a box of longs, they'll cost as much or more than long rifles, so the long is rather pointless.
But anyway, you wanna shoot shorts in a 22 autoloader- go ahead, won't hurt a thing. If you do fire many shorts in an autoloader, clean the chamber afterward- shorts tend to carbon up the forward part of the chamber, and the dirty chamber may hurt cycling of 22 long rifles later.