It would have been different if you had drawn a Cultist from the 4 draws generated by the 2 Cultist playings
The moment you are trashing the Cultist for Procession, the playing of Cultists is over. Procession is
1) play card X from your hand
2) play card X again
3) trash card X.
Point 3 triggered you drawing 3 cards, including 2 Cultists. A Cultist chain can exist only because you can play a Cultist as part of the resolution of another Cultist already being played:
+2 Cards. ... You may play a Cultist from your hand.
When you had drawn the 2 Cultists, you were already at point 3 of Procession's effect, so no Cultist was in the process of being played, so nothing gave you the ability to "just play" a Cultist.
If you had drawn one or more Cultists earlier, that would have been either during 1) or 2) above. That means they would have been in your hand when the 2) playing of Cultist comes to the point where it allows you to play another Cultist, so you could have continued the chain.