they definitely don't. Search for "ᴜɴɪᴄᴏᴅᴇ ᴛᴇxᴛ" and you'll see the only matches are exactly that.
They usually don't, because the text isn't supposed to be equivalent to "non-'Unicode'" text.
Google does, atleast for fullwidth.
Which makes sense, as fullwidth is likely to be accidentally typed when using a Chinese/Japanese/Korean IME, and is entirely equivalent to normal characters, it just fits in with CJK text layouts better.