The consequences are the consequences of playing two characters in simultaneous superposition.
There's nothing a Fate Accelerated character can do that a Fate Core character can't. The opposite is also true. Approaches and Skills are both intended to exhaustively divide up the available action space. If you feel like you need a refresher on either system, absolutely bone up on them online. You're trying to make some kind of hybrid system involving both of them, and you should absolutely have as good an understanding of both of them as you can before you start trying to stitch one to the other.
All the same, having an idea of things to consider can't hurt when you're doing the review, so here you go.
I'm assuming, since you haven't said otherwise, that there isn't a separate magical world and mundane world - there's just one world, right? There might be a few things too magical to be mundanely understood and a few places where magic is weak or gone, but by and large people can point either skill set at most of the problems they expect to have, right? Effectively you're making a magic character that does magic (with Fate Accelerated) and a mundane character that uses regular skills (with Fate Core) and you're playing them both at the same time.
The problems with this are going to manifest in two ways: struggling over resources and deciding who to play when.
Struggling Over Resources, a.k.a. Dukin' It Out
Oddly enough, Fate Points are not going to be a scarce resource here. Fate Points have to last you one session over all the time you have, and you haven't said anything about needing to use magic and mundane skills simultaneously. So you've got the same amount of character focus time to budget your Fate Points over, they're not really a big deal. The big deals are Aspects, Stunts, and Advancement.
Aspects. A full load of 5 aspects on both characters is probably too much to stay focused on - and this is the same character we're talking about in both cases, right? I'd suggest a standard 5 and then a high concept/trouble (or, if you'd rather, strength/weakness or function/flaw) for the magic knowledge specifically.
Stunts. ...and, I suppose, starting refresh, since they're kind of linked. Not all stunts are necessarily related to a skill - stunts that let you do things 1/session without rolling could as easily be magic or mundane. You'll need to make the call there, if the standard 3/3 free is enough or if you want to say, like, 4 free but you have to have at least one magic and one mundane?
Advancement. Do you have to pick between mundane skills and magic when you hit a milestone that lets you advance one? You could to set up some different milestone expectations between what improves your mundane skills and what improves your magic skills, and it's also worth considering the expectations for what improves your refresh (in either case) and spend refresh on linked stunts.
Deciding Who To Play When
Even after you've got the specifics of character creation sorted there's still the issue of when these skills will see use in play. So there are considerations of peaks, of encapsulation, and of a price to pay.
Peaks - Absolute Number Bigness. Accelerated characters start with a +3 highest approach, Core characters with a +4 highest skill. This is probably fine if you intend a mundane specialization to be stronger than the associated magic, at least at the start without milestones or a stunt to reinforce it.
Encapsulation - Relative Number Bigness. While Accelerated and Core provide two different ways of dividing up available activities, and while there's not like strict encapsulation in the sense that you could just as well Cleverly Deceive, Flashily Deceive, or Sneakily Deceive somebody, it's kind of hard for me just to say a priori exactly what uses of, say, Burglary, Deceive, and Stealth couldn't be handled by some Sneaky Magic. Depending on how character creation goes, you could find yourself in a situation where your magic just can't do better than the skills you might bring to bear instead, or vice-versa.
The Price to Pay - Separate Worlds
Yeah, this one gets its own big-boy header, because it's basically the frame challenge to the above considerations - ways to make magic and mundane skills operate differently on the same world.
Impractical Magic. Your magic skills represent a level of knowledge and capability best described as "abstract". Actually applying magic to your problems takes some time and care, either in play or on your character sheet. This basically borrows the idea of invention from the Atomic Robo setting, where Science is a similarly constrained skill. Using magic to create an effect in the world requires either devoting one or more stunts to a "magic item" which allows that magic to fill in for a mundane skill, or a "spellcrafting" process that effectively creates a temporary magic item at a cost that goes into the GM's fate point reserve.
Less Than Two Characters - Specialist Wizards. Most fictional wizards aren't really generalists. Mirror mage, shadow mage, fire mage, ice mage -- they're known for a narrow slice of capability or a few signature spells. In cases where people are creating maybe the party's only reliable arcane ally, it makes sense for character creation to effectively give them a bunch of specialties, but when everyone is already a wizard, do they all still have to be varying degrees of generalist? You might consider something like The Six Viziers from the Fate System Toolkit, a way of giving people magical gifts that enhance the skills their characters may already focus on.
Less Than Two Characters - Mundane Specialists. If, on the other hand, you do want a party of generalist mages, you might consider using the regular core skill list to represent just a few focused specialties, perhaps just giving people a singular 4/3/2/1 skill column in addition to their full Accelerated spread of magic.