On my first reading I had concluded that you couldn't use the bladesong in wild shape, although in re-reading I don't see anything that explicitly forbids it. That said, I think a DM would be within his rights to declare a sword dance something your beast form is not capable of doing; I probably would.
The benefits themselves feel a bit lackluster to warrant the level dip; the concentration bonus is nice, but you get no benefit of stacking int outside of the AC boost, and you're pretty MAD, wanting dex, con, wis and int. I think both monk and warlock (always-on mage armor) would be superior, but it could work.