Very likely, as it can cut through steel or freaking meteors with ease.
However, Doffy would never do that since he can't swim.
Yet it couldn't even cut through these buildings. Unless these buildings are for whatever reason more durable than an island or made of seastone like the factory(both of which seem unlikely), birdcage is inconsistent, making it an unreliable feat. Inconsistnency aside, all of this assumes that DD can make a birdcage large enough to contain the whole island in the first place, which there is no proof of. Likewise, as far as we know the island would take at least an hour to cut, which I wouldn't necessarily call "island busting". As it stands, maybe the possibility exists, but the feats don't convince me of it.
Edited by Leper, 16 November 2015 - 01:20 PM.