Hmm interesting would it be more or less interesting to you to see him live passed 1183 and ascend the throne as Henry III with his son William around as his heir? Would his son's surivval in 1177 butterfly the war that killed him otl?
Well, Henry II is imo England's version of Stupor Mundi, just and endlessly interesting (and interested) figure chalk full of over the top talents but also complete with almost Shakespearean tragic flaws. I'm always tempted to oversimplify it and think of it like a play: genius young king, limitless talent, energy and ambition, but greatly wounded early by trusting a loved one too much (Beckett) and therefore later undone by trusting too little those closest to him. And I mean, I think that largely holds true, but obviously there are umpteen more layers/wrinkles. Anyways, my point is that I think an element of the tragic cycle was probably inevitable, in that Henry raised a brood of ultra-ambitious, largely talented sons but who always strained at the bit because of his style of hands-on personal rule over an ever expanding empire. I actually think Henry the Younger's personality might to a degree have kept things off the front burner...He almost won his first rebellion, and after that seems to have been (for a Plantagenet) relatively content with becoming the family rock star while holding only honorific titles.
I think, for example, a Richard or Geoffrey in his position would have rebelled endlessly until dead or triumphant, especially with Alienore stirring the pot as ever. I think any peace would just be brief interruptions in the pattern. And I think we see this later on after Richard does become heir apparent. So maybe Henry living longer means greater gaps in familial warfare. But if/when he does become king we might see another Anarchy or earlier WotR. He's too popular to be imprisoned for life a la Curtmantle, so even if Rick/Jeff win, it'd just be the same pattern if he lives, with his supporters rebelling in his name. Otoh, unless the sources are unkind, he's outmatched by his younger brothers above the shoulders and lacking the same measure of insatiable need for more, so I don't see him putting it to bed either.
I could (and do) speculate endlessly about this family, and like the similar dynamics (House of Normandy, later house of York) where you get talented ambitious brothers full of personality and drama I think it was always wide open to all kinds of alternate paths. I think HtYK is maybe the least dynamic of these, but that might just be due to his dying before more could happen, and even if true his relative phlegmatic nature adds another spice to the pot.
Edit: oh, and about William, it's petty tabula rasa, obviously. The only point of interest being the possibility that he was Marshall's son...though the cuckold meme was a pretty common rumour about any 'affable' feudal leader, there might actually be something to this one. Something of note seems to have occurred between HtYK and WM, and this is one of the rare instances where Marshall seems largely to have been considered the villain of the piece. Some believe it was just him relying too much on Htyk's affability and forgetting his place, but who knows.
Yet another edit: absolute best case scenario imo is HtYK having settled into the role of family front man is satisfied with getting his hands on actual land/incomes as king and is happy leaving the actual governing to his brothers, and that they are also satisfied with same. I think the first part is possible, but I have serious doubts about the second.