ABSOLUTELY ... I have a goodly number of the Savages from that era. A couple 19s, 23s, 23As, 23AAs and they are sweet, old rifles ... from the way-back time.
Clean it up and enjoy your new time machine! (and tell us how she shoots)
It is very rare that any .22 rifle is unsafe to shoot. Bolt actions in general are very safe. Whether or not any old rifle functions properly is a matter of past treatment.
Basically, clean your rifle, very lightly oil it against rust and enjoy the shooting.
