Can't agree, really. Percy likely surrendered because Richard was killed; he'd been untouched and was in a position to retreat, but wha' the point with no king? So hat's 4000 right there, unbloodied. And I strongly disagree with the notion that most of his support was there; he's been second guessed specifically because he fought without waiting for most of his northern forces, particularly Yorkshiremen. The City of York itself long lamented the fact that they'd not been there on the day. And there's Ireland, long a Yorkist stronghold and Burgundy would likely match French contributions if needed.
Without a reigning king in the field and after 2 years of winnowing, the Yorks still raised almost 10,000 for Stoke, remember.
If the Yorkists lose, Percy's army isn't going anywhere; Henry's priorities will be to secure the king, and he certainly has the troops to defeat Percy before he can meet up with reinforcements. Most likely at this point, if Percy has Richard, he turns him over to Henry in exchange for being forgiven for opposing him. If he doesn't have Richard, he still makes whatever peace he can; he's not in a good position to continue resistance, and he's just seen Richard's main army be routed. The Tudors will absolutely pursue Percy's forces if they continue to resist; their commanders are certainly capable enough for that, and if Percy finds himself outnumbered and surrounded, he has little choice.
Certainly Burgundy, Ireland, etc. can raise additional troops if given time, but Richard needs them
now if he's to avoid becoming a hunted fugitive.
Nor can I agree that he's a pretender; he's been crowned, and ruled for 2 years. He may very well become one if his support falls away and he's forced into exile, but that's not the default result of losing one battle. It may happen, it may not. I will agree that the South largely saw him as a Northerner, and as such didn't hold any particular affection for him, but they knew Henry Tudor even less, and his marching in backed by French mercenaries and Welshmen isn't going to be particularly popular if there's an English king out there. How London will react is anyone's guess.
I again reiterate that the immediate ramifications hinge so much on Percy. If he betrayed Richard, than I agree Richard at best retreats to the North to build an army, or possibly Ireland or Burgundy and Henry likely takes London. But if, as he maintained, it was just that he was impeded, Northumberland's 4000 immediately form the core of an army the northerners can build on, and I'm not sure Henry can safely march on London with the kind of army he's leading. And this is all supposing that Richard's van and center are completely wiped out; 5000 of the non-Percy contingent survived as is; supposing it went better enough for Richard to withdraw could also mean he leaves with 2-3000 to link up with Percy's 4000 and battle is resumed fairly soon, with northern reinforcements on the way.
Defeated armies in the Wars of the Roses rarely retreated in good order; if Richard is truly defeated (which I take to be the POD), he's not reforming his army anytime soon. OTL, quite a few escaped due to Richard's death-or-glory charge leaving them behind; if he loses but still survives, the POD essentially requires him not to launch said charge, in which case his army is going to have a much more difficult time disengaging safely. If nothing else, Henry's surviving army is (by assumption, given that he won ITTL) significantly larger than what's left of Richard's, and with a significant victory under his wing, is likely to attract more supporters who see the way the wind is shifting, while Richard's army will be severely demoralized. Henry already has the most significant nobles either on his side (the Stanleys) or dead/defeated (Percy, Howard); Richard needs time to build an army to replace the one he mostly lost. At best, he escapes to the north with Percy and whatever troops he can salvage, but doing so essentially concedes the more populous south, and automatically confers significant legitimacy to Henry.
As for the question of whether he's a pretender or not, that's mostly semantics, but if he's been badly defeated and driven away from London, he's certainly not the uncontested symbol of legitimacy.
