I've had a bit of a look at Henry Holland for an upcoming article as part of my War of the Roses series on the SLP blog.
I think some permutation of Exeter Jnr gets involved in the rebellion against Richard in 1483, goes into exile, plots with the other anti-Richard exiles and potentially the Lancastrian dregs still roaming around, and launches an invasion in a few years when Richard's regime is looking shaking, is broadly plausible.
If we're going with the 1461 birthdate then he'd be 22, possibly still unmarried, and can pledge to marry Elizabeth of York and unite the claims. I don't think the first cousin thing would be too big an impediment, unless the Pope has some reason to be obstructionary.
A Holland-centric invasion probably goes through the West Country, given that was the centre of Holland influence, so that'd effect the geography of any campaign against Richard, probably having both advantages and disadvantages compared to the Tudor route through Wales.
The important question is probably how the existence of Exeter Jnr as a plausible (arguably pre-eminent) Lancastrian claimant effects the behaviour of both Marg Beaufort (and by extension the Tudors) and Buckingham in 1483. This goes into the murky motives of Buckingham- if he was aiming at the throne, would he still entertain that delusion if there's a legitimate Lancastrian candidate in England? If his motive was ''this rebellion looks serious, Richard's doomed, I'm jumping off a sinking ship'' then he might behave as OTL. As for Marg, restoration of Henry Tudor as Earl of Richmond would be compatible with a King Exeter, is that enough for her to risk her head?
Arguably if things go right Exeter might be able to find his way to the throne with the Rebellion in 1483, being a potentially more powerful rallying figure than the exiled Tudor and the uninspiring dolt Buckingham, but if he messes up he could also lose his head. Alternately, if he stays loyal to his uncle- you could sprinkle in some dislike for the Woodvilles or some territorial rivalry with Dorset (if Dorset still marries Cecily Bonville he and Exeter would have interests in the same area?)- he might also potentially be in the running to be named heir after Edward of Middleham dies.