Who knows, maybe the reorganized Section 31 joined forces with the Zhat Vash after all that unpleasantness with Control. It started out as their own strategic AI after all...
Yes it is possible, the only issue blocking it is time, it will require Burnham, Georgiou or possibly her mother to travel back in time a very long way using the suit.
Plus for the cycle to start it will require that person to have the images in their head so they can go back and transfer it to the Vulcans in the first place.
It may not have anything to do with Control and Discovery but it is looking a bit fishy to me.
I could totally see the Commodore as S31 but there are going to be some unhappy campers if it ends up being true.
I will be OK with it but I can certainly understand why so many want Picard to be its own thing.
Plus I think Discovery is heading for a colossal reset anyway, its funny really, Burnham could go hunting through time to find the events that brought about the war with the Klingons and the fall of the Federation, in so doing she would end up having to wipe herself from existence to make it happen, the suit would protect her from being erased but she would have to go somewhere that is guaranteed not to cause problems.
One of the best places she could go is actually back in time a long way rather than forwards, thus letting the Vulcans know about synthetic research in advance.
There is still the matter of the Supernova and how that happened is the real question that will lead to the true big bad of the series.