I'm assuming you were making a joke here, as G/A are from the 32nd century and PIC takes place in the 24th/25th century. If there's even a hint of small-universe syndrome with that lineage, it would be that Vadic is Grey's or Adira's great-great-great-great-great-great-great-great-great-great-grandmother, give or take a generation or three.
Wild theory- maybe Vadic is Vash and Picards daughter? Combining names- Vash= Va Picard= dic Most likely though she’s someone who had a beef with Picard off screen so it will be a whole new storyline.
I'm going to put in one more guess that the plot involves the brain worms from Conspiracy. In a Trek Central interview Matalas said that Vadic was aware of Picard, but not after him in particular. Conspiracy worms seem unlikely for a couple of reasons. Their advantage is to stealthy infiltrate by taking over hosts, not blow up Federation HQs or hijack Vadic. They only reason I'm guessing this at all is it's a big loose thread from the TNG era never followed up on and that Robert Meyer Burnett seems giddy at the deep lore and understanding of TNG put towards the season. Personally, I'm not hoping for brain worms, but it seems plausible.
I would definitely like to revisit the Conspiracy brain-worms. The clicking alien abductors from Schisms (known as the "Solonae" in ST Online) would also be a good one to use. Remember there was that little white dot that escaped the mini-wormhole after it closed at the end. Something's still out there...
RMB has also mentioned on Twitter there’s a tie in to the Shatner novel “The Return” in S3. Can’t remember if it’s been discussed already what that could be. My guess would be Spoiler That V’Ger was linked to the Borg Only because I can’t think of anything else meaningful. Can’t imagine they are going to reference Kirk being alive. Or maybe there will be a Defiant-class USS Monitor flying about.
I could see it having more to do with salvaging the Enterprise saucer from Veridian III more than anything else. Or the Borg dog drones. Those were cool.
I'm going with they salvaged the Enterprise-D saucer. If they don't get if off of there, then: Eventually those Veridian IV inhabitants might develop telescopes and spaceflight, and travel to Veridian III before they achieve Warp Drive. Then they'd see the ruins of this advanced ancient ship.
The more I look at this the more the dates suggest: Vadic is the child of another 1701C crewmember who was already pregnant at the time of Narendra III) Tasha adopts the child as her mother dies during or after childbirth. Child has a shitty life (perhaps ends up on Remus as well). This links up with Amanda Plummer's age / that of Vadic and her motivation is simply that her life would have been very different if the ship had not been sent back.
Oh - a bit narcissistic replying to myself. But if flashbacks are used, then it could potentially allow Denise Crosby to be featured - either as Yar or as Sela - if de-aged - or even Sela as currently since we don't know when Sela died? Of course Matalas would deny Crosby's involvement in order to mask the plot or reduce speculations.
Just saw the football trailer. Spoiler Vadic has funky veins on her face like Shinzon before he died. So I’m thinking…FEMALE PICARD CLONE
As I posted earlier (and others have as well), I'm betting Vadic is related to Tasha Yar and had been held against her will by Romulans. Basically, S3 (or the Vadic subplot) will be Nemesis rebooted.