The question did not ask if the theory was correct. It asked if there was any evidence supporting it (vs. refuting it).
Despite the evidence listed below, I don't think the theory is correct, for a variety of reasons that contradict it, including Occam's razor as well as word of god (JJ Abrams).
I don't know of any canon in-universe evidence to support that theory with any degree of certainty.
However, breaching the Fourth Wall, there is some evidence to support the theory:
A LOT LOT LOT of the new Disney canon seems to be - deliberately or not - mirroring Original Trilogy, in great detail.
He tells Vader's helmet "
I will finish what you started".
So, what exactly DID Vader start?
- Start as emo unbalanced teenager. Check
- Betray your Jedi friends and teachers. Check
- Murder other Jedi students and all Jedi. Check
- Join the Dark Side (Sith in his case) as main apprentice to main Dark Sider. Check
- Bicker with the Dark Lord's highest military figure over the Force vs. Military Force. Check.
- Kidnap a powerful female Force User (preferably, of Skywalker Bloodline, your relative). Check (relative part is likely but uncertain).
- Try to get location of important Rebel info from kidnaped powerful female Force User, only to lose her when she's busted out by Han Solo brandishig blasters from Millenium Falcon? Check, mostly.
- Murder a bunch of innocent people so your Dark/Sith master thinks you're on his side. Check.
- Betray and murder your father? (according to Obi-Wan Kenobi). Check
- Bring balance to the Force, by betraying and murdering your Dark/Sith master: Episodes VIII or rather IX?