Seems like it shouldn't be too difficult of a stretch. It sort of depends on how deep you want to go.
First: you could always just add backgrounds onto existing Numenera characters and call it DONE. There's not really any sort of major "balance" mechanic this would hurt; the gamebook itself says, more or less, that if you add a bunch of stuff onto your PCs and they're more powerful but the story is still fun, then who cares? Mechanically, you could say whatever their backgrounds are, they are "trained" in that for Numenera. (If they were really, REALLY good at it, they'd be specialized.) Numenera skills are already completely undefined and as broad as you'd like, so it seems like it would fit well.
If you're looking for more of a "balance," it's already within the rules to add skills (backgrounds) to a character for the cost of adding "inabilities", or skills in which the characters have disadvantages. So you could also require that each background in which someone is trained also necessitates an inability to mitigate it. I wouldn't get more technical than that, but you could even loosely define "broad" vs. "narrow" skills, and trade 2 narrow for 1 broad, or even-for-even, or whatever.
Also, each Numerera character gets a descriptor. These broad-based ideas typically involve skill suggestions. You could always incorporate the characters' backgrounds into their descriptors and broaden them out generally in the same ways above. We definitely did this when creating characters. For example, we took "swift" and changed it around because the balance inability seemed incongruous with the PC's character, and we wanted to add some other stuff, too.
Overall I would think those two systems could come together well.