Yes, the Soviet papasha (PPSh-41) is allowed as a main match rifle if it's operating under 1400fps.
Here's a direct quote from the rules:
"Any .30 caliber or larger caliber pistol, .30 caliber or larger pistol cartridge firing rifle (straight cased; eg, .351 Winchester)"
The first part of the sentence talks about pistols and states:
"Any .30 caliber or larger caliber pistol, "
Another part of the rules limits pistols to 1200fps, so you may have to do some creative reloading to meet the velocity restrictions for the Tokarov pistol, but it can be done.
Any .30 pistol caliber pistol round (straight or bottleneck) or larger pistol round is allowed when fired from a pistol within the 1200fps velocity restrictions and those same rounds are allowed if fired from a main match rifle if they are under 1400fps out of the rifle's longer barrel.
The true reloading challenge is where the second half of the sentence speaks to main match rifles where it also allows:
".30 caliber or larger pistol cartridge firing rifle (straight cased; eg, .351 Winchester) "
This makes exceptions for pistol caliber main match rifles and allows for rifles that chamber straight wall rifle rounds like the .351 WSL (.30 Carbine, .401 WSL and several others) that were never designed as pistol rounds.
These rifles / rounds were designed to function at velocities well above the 1400fps rifle velocity restriction allowed in the rules. AZSA competitors have overcome the original design restrictions of both guns reloading with very slow burning powders or heavier bullets or both.
Hope this helps in understanding the rules.