It would have made a difference because it would have created a huge plothole in the actual story.
During the era of BBS the walls of the worlds were still intact and Heartless could not enter the Realm of Light of their own volition. Only absolute Masters of Darkness like Master Xehanort could summon small amounts of them, not to mention Emblem Heartless didn't even exist at that point in time.
It were the experiments done by Xehanort and Ansem's Apprentices which resulted in the Emblem Heartless being created and the ability for Purebloods to enter the Realm of Light on their own whim, all which happened after BBS.
Well, hold on about that.
By the time of BbS, the empty space between worlds in the universe is just a pool of Darkness, arguably created during the War. Consindering I don't think such a catastrophic event unfolded without unleashing the Heartless floodgate, and that Emblem Heartless are a thing even in Chi (wether or not they're all part of the Book's illusions is still kind of a grey area), I wouldn't put them out of commission like that.
Heartless do lurk in every dark corner, as Yen Sid says.
That's that. But even if you're correct about this:
Yen Sid claims that the Heartless will exist as long as there's Darkness in every heart, and thus it'll be difficult to get rid of them. I don't think he would say "difficult to get rid of them" if they only stayed in the Realm of Darkness.
And, Eraqus did unlock the Lanes, just like Sora will do later in KH II, and the Heartless will use those passages.
On behalf of these things, I say you could definitely tweak things not even that much and make it so Heartless in BbS aren't a plothole at all.
And yes, I'm also part of the No Unversed faction. Ugly, uncreative, and their italian names are stupid as heck.
