Would there be any reason not to do this, especially is one prefers the era of Arthur to Uther? I mean it is in the very name, King Arthur Pendragon, and I don't really get the focus being put on Uther. Would the Great Pendragon Campaign still be useful to use, and what other publications would be recommended?

No particular reason why you couldn't. The old Boy King supplement did just that. GPC includes pretty much everything from that (I didn't check, but that is my memory of the two), except GPC goes even more into detail. I think the Boy King tapers off as far as the events go after 530. GPC has the full run all the way to Camlann, so it is superior in that regard. Heavier, too, obviously. :)

The only downside is that you miss out on the Anarchy, which is perhaps the most interesting period in my opinion. But if you want to play an ARTHURIAN saga, with knight errantry rather than fight hordes of Saxons, then yes, feel free to skip.

Any adventures in particular you might recommend to go along with a campaign within the Boy King era? I have heard praise for The Grey Knight.

The Spectre King, Tounament of Dreams, and the Heart Blade (in Blood and Lust) look really good. I haven't progressed far enough in the GPC to run them yet though.

The Spectre King, Tounament of Dreams, and the Heart Blade (in Blood and Lust) look really good. I haven't progressed far enough in the GPC to run them yet though.

The Spectre King is a great story, but very very very (did I say very?) deadly. You'll basically need everything to go exactly right to defeat the Spectre King, or you will have a Total Party Kill in your hands. Also, its stated timeframe is well to the conquest 525 onwards (Vortimer is born in 460 and is stated to be between 65 and 105 years old). Given that The Spectre King references things like partial plate mails and destriers, the earliest would be mid-530s or even better, early 540s. Personally, I'd be tempted to spring it on any survivors of the Boy King and the Conquest Periods, in the hopes that those knights would have enough Glory and Skill to manage against this terrible foe, or, in the absence of that, give a chance to have some old knights die heroically and clear the table for their heirs.

Heart Blade is an excellent adventure, in my opinion, and very well suitable for the Romance Period (530s). Sir Amren should be introduced earlier, though.

The Grey Knight is explicitly intended to happen in 515. However, please be aware that there are some issues with it, like the skill levels of the knights mentioned, and that Gaheris is way too young to be a knight already in 515. Even Agravaine is kind of pushing it, in his late teens or so.

Tournament of Dreams could be another possibility during the Boy King, but you are getting swamped a bit timewise (510 -513 Unification War, 514 Arthur's Wedding, 515 The Grey Knight, 516-518 Saxon War). You could wait until the start of the Conquest Period, like 519-520.

The Cambrian War, especially its PK-centric Bulith (sic, should be Builth) War, is another very nice multi-year scenario from The Savage Mountains (which has a bunch of other adventures, too). My preference would be to play it during the Romance Period: this gives enough time to fit in the Tournament of Dream in Conquest, while also having enough time for Belinans to switch from pro-Arthur (in ToD) to more hostile (in CW). I'd probably time it to start around the middle of the period, hence giving time for the PKs to be adventuring in Cambria earlier and maybe make some friends and allies, as well as start ramping up the tensions.

Like said, you probably won't have so much time for big adventures during the Boy King Period, due to all the battles going on. However, another multi-year scenario would be the 'Of Allies and Enemies' (AKA Oxford Usurpers in a reduced format in GPC p. 96-97) in Lordly Domains. This would be a good scenario to use during the Boy King 514 - 515, since the Saxon threat is being referenced. My preference is to run it at the start of Anarchy, but if you are skipping straight to the start of the Boy King, then right after the Battle of Terrabil would be my choice. Let the PKs participate in the Wedding and then get whisked off to Rydychan to help out. They should be able to wrap that up by Autumn 515, and pushing the Grey Knight (and Arthur's penance) to 516 shouldn't be too bad. Alternatively, you could run Oxford Usurpers scenario 511 - 512, missing the Battle of the Bassus River (512) and the exile of Balin (but since that is a 'witnessed event' rather than an adventure, no big loss), but then you don't have to amend the Grey Knight at all. However, in my opinion, if you start the campaign at 510, the Player-knights are way too junior in 511-512 to be trusted a leadership role like that in the 'Of Allies and Enemies'. After the Unification War, then yes, they might have racked up some significant Glory and might be more experienced to take the lead in 514-515. Also, Ulfius' preoccupation (in LD version) is with the Saxons, not with the rebellious kings, which fits 514-515 better, too.

EDIT: Just to add to the above... If you are running it as a quick 'Duke Ulfius and Count Robert join forces and kick the usurpers out' rather than an extended scenario with PKs in quite independent command (as it is in LD), then Year 511 works just fine.

I think there was someone who posted a suggested timeline with all the adventures in it, but I can't recall of the top of my head what the thread was.

Grey Knight is a great great adventure