Oh yes. That's known as the .223 Timbs, though the standard .308-.311 bore diameter barrel of the 7,63mm Mauser *Broomhandle*, the Czech Vz52 rollerlocked pistol, or the Soviet 7,62x25mm TT-30 or TT-33 Tokarev pistols are most commonly used, though I've also seen a .38 Super Colt Commander so reworked. And it can also be done with 7,62x25 machinepistols with longer barrels, raising velocities even higher. The Soviet PPSh-41 with 71-round drum magazine is particularly sporty in this respect.
Depending on the strength of the particular pistol used, velocities can range in the 1750-2000 fps range, using a 50 or 55-grain bullet. It's also possible to use the heavier .224 jacketed bullets of the SS109 5,56mm ammunition, or that of the 5,45mm Soviet AK74 cartridge.
One minor downside has been the inavailability of tracer ammunition, since the plastic sabot fitted around the base of the cartridge precludes ignition from the burning powder charge. But a couple of possible alternatives are under consideration and may work out.
WAG: lock the sabot to the bullet via grooves in the bullet (and mating ridges in the sabot halves), rather than surrounding the base with plastic.
I had a Tokareve once. Creepy gun, I always wondered if it had hung on an NKVD officer's belt, if it had been used to put a bullet in any prisoners' necks. And no safety! Just "half cock."