It would be hard in 4e.
Mostly this is because monster powers are not really balanced for PC use...at. all. A monster encounter has no relationship in power to a PC's encounter power. They are, essentially, totally different effects.
If you had a suite of monsters specifically designed to be used in a campaign with this character, it could work, but only if you used only those monsters. The moment you want to add in a monster from any other source, a wrench gets tossed in the works.
Add to that this: the mechanics of Blue Magic have always been really wonky. In addition to being very difficult to get (the right monster has to use the right ability on the right character, usually requiring charms or the like), the magic a Blue Mage received could be anything from awesome to blah. They aren't reliable, and they aren't well balanced, and, well, that's kind of the fun of them.

But in a Final Fantasy game, if you have one useless character, it's not the end of the world -- you've usually got 2-4 other useful characters to use. And if you discover an exploit, it's kind of fun, since you can now win whenever you want to. In a tabletop game, if your character is useless, it can be the dullest experience in the world, and if you find an exploit, it can ruin the game.
In
FFZ right now, largely because of that last reason, blue magic is, essentially, a "treasure." You aren't allowed to base your entire gaming experience around the abilities of your enemies, because it's not nearly as fun to do if it is the only thing you can ever do.
That cautionary tale aside, though, I don't want to burst the bubble of your cool idea too hard. Give it a spin if you want, and have fun.

Just be cognizant of the fact that, for instance, such a character doesn't even have a useful
combat role, nevermind that every power he gets might just fall into only two categories: useless and overpowered.
That's fine for a treasure award in FFZ -- those are extras on top of your character anyway. It's not so fine as the main focus of your character.
Best way to play a "blue mage like" character in 4e is to become an Enchanter or a Psion, and focus on powers that make your enemies hit each other.
You might, thematically, want to consider a Druid, as well. "Beast Form" powers could easily be fluffed as monster powers. It wouldn't be very mechanically similar, but re-fluffing is pretty easy in 4e, so there is that option.