The Void would devour the entire world, including the Shadow Isles.
"Our darkness will blot out the sun of Runeterra."
But in all seriousness, I think the Void, being an extra-dimensional world-eater realm would consume the Shadow Idles along with the rest of the world. Only one type of magic could repel them, and that magic has since been forgotten. And even then, it could only make a temporary barrier against the Voidborn.
The Void is always evolving, as evident with Cho'Gath, Kog'Maw, and Kha'Zix, as they've managed to overcome that special magic that repeled them before. As badass as the Shadow Isles are, I have no doubt a realm of extra-dimensional, ever-evolving, nightmare monstrosities could devour them. The Void consumes entire worlds and the Shadow Isles are simply a small part of that world.
And since the Void shares some Lovecraftian themes and the Shadow Isles revolves around death:
"That which is not dead can eternal lie, And with stange aeons even death may die."
The darkness of the Void will make even the dead of the Shadow Isles know fear again. There's only one world of light, let the one darkness destroy it.
On a side-note, a Void-Shadow Isles hybrid would be truly terrifying. Either a Voidborn dies and is resurrected in the Shadow Isles, or an undead spirit enters the Void and succumbs to its corruption.