It all depends on what you consider to be core to Blue Mage.
In my opinion, as long as it's a job that learns monster abilities and uses them as a core mechanic, it's a Blue Mage. The specifics of HOW they learn them are VERY flexible. With those requirements, it would be EASY to fit a Blue Mage into this game.
Others have a MUCH longer list of requirements for Blue Mage, many of which are specific to only a few or even just one of the other games in the franchise. Some insist that a BLU must be struck by the ability to learn it (this shows up in some FF games, but notably not VIII, XI, X, or XI). Some insist Blue must have hundreds of skills of which you can equip only a limited number at a time (this trait is unique to ONLY FFXI BLU). Some insist that you must be in combat with the monster to learn the spell (this was not a requirement in VIII; you could acquire the blue magic item without Quistis in combat and feed it to her later). Some say that learning a spell should be up to RNG - that you only have a CHANCE to learn, even if the mob uses the spell (this is found in only XI, and arguably VIII since the blue magic item only has a chance of dropping).
BLUs have a rich and varied history in Final Fantasy. The core nature of their job has never changed, but the implementation has changed, often radically, from game to game. It would have its own implementation and identity in FFXIV, as well; whether that implementation will suit your tastes depends a lot on what you believe is essential to a Blue Mage. Just be aware that what you consider to be essential is not necessarily what others do - and if what you consider to be essential is flat-out incompatible with the way jobs are implemented in this game, well, you will be disappointed. Frankly, though, your being disappointed is a small price to pay if the alternative is to leave BLU out of the game entirely.