No. Here's the biggest Warhammer 40k secret: That's not The Emperor on The Golden Throne. It's Alpharius.
/jk
But there are some questions I'd like to see answered at some point.
But how deep IS the Alpha Legion infiltration? We know they've had operatives in all the loyalist AND traitor legions since the Heresy (on a side note, I feel sorry for the poor bastards to got assigned to infiltrate the Death Guard, Thousand Sons, and the Emperor's Children), but the question is "does it stop there?" Imagine AL operatives in the Inquisition or in the Custodes. Do I even dare suggest there are AL operatives within the Sisters of Battle? What if an Alpha Legionnaire took the ultimate plunge to become a Daemon Prince for the sole purpose of subterfuge and sabotage on the Ruinous Powers?
I honestly believe if there was a CSM Legion that was capable of getting their hands on the data to make a Primaris CSM, it would be the Alpha Legion. The question is, would would they share it with (if they would share it)?