The girl being the sword is pretty likely. There is one thing I have to say though, why are we all assuming that she turns into the Master Sword?
If this is a new Link, then yeah, she's probably the Master Sword (Mistress Sword?), but if this is the same Link as was in Twilight Princess, which I believe it probably is as every Link in the past got 2 games released fairly close to each other and TP Link hasn't got a second game yet, then it may possibly be an entirely new sword that she turns into. I say this because look at the previous 2nd LoZs from after the Master Sword was created, they were always new swords, yet similar to the Master Sword.
Link's Awakening - LV2 Sword*
Majora's Mask - Gilded Sword
Phantom Hourglass - Phantom Sword
*The LV2 Sword was named after the Master Sword in LADX.
I do hope that she is the Spirit of the Master Sword though, the story of the Master Sword really needs to be fleshed out beyond that it was created by Ancient Hylians to slay evil.