As Gregor explained, simultaneous games (sometimes abbreviated "simuls") are quite common at Go tournaments or exhibitions at which pros (or very strong amateurs) are present (example). The teacher is often booked specifically for lessons and simuls, with prices typically ranging (very roughly) in the lower 3 digits (this is often one of the main cash sources for strong players living in the West).
The rules specific to simuls are, as far as I know, very similar to chess: Pro walks from board to board, players have to move when (or possibly before) he arrives.
Blind Go in the sense of "no board in use" is virtually never practiced. It is tough in chess, and almost impossible in Go: Even the strongest players cannot precisely remember the large (19x19) board, a notable exception being the Asian 6 dan amateur Bao Yun, who is said to compete almost as well in blind Go as with full vision.
There are many variations of "blind", though, for instance "Go for the visually impaired", which has eyes closed, but players are allowed to touch the board and feel the stones (special boards and stones are used for this purpose, black and white have a different surface). This is at times used in exhibitions (for instance I've seen it between a Japanese pro and a visually impaired Western amateur during the EGC 2011 in France, of which I sadly could not find the video), but very rare and not in conjunction with simuls.
More well known, however, is one color Go, in which both players use only stones of one color to play; they have to remember which stone belongs to which player. This is incomparably easier than fully blind Go, most dan players should be able to do it at least on small boards. If you're used to it, it's not difficult even in full-length 19x19 (I, as a low dan amateur, often play this for fun). Still, in simultaneous games, even one color Go is practically unheard of.