It's happened twice to me, and it's always very strange.
Once during Hairspray, Curt Hansen took over for Constantine Rousoli as Link. Constantine left after "It Takes Two", and Curt walked on as Link for the dodge ball scene. The audience was very confused at first, but an announcement was made at intermission.
During opening night of the Wicked tour in Philly just a few months ago, Alison Luff left after receiving the hat from Glinda, and Laurel Harris (the standby Elphaba) made her entrance when Elphaba arrives at the Ozdust. It was confusing, because Laurel took over half hour into the show, but the announcement about her being on (and her name being placed on the understudy board) didn't get made until intermission, when she had in fact done more than half the show.
With Curt and Constantine, I knew immediately they had switched, but with Alison and Laurel, it was a little more difficult to notice, even if I began to notice she did look different and sound different.
"Anybody that goes to the theater, I think we’re all misfits, so we ended up on stage or in the audience.” --- Patti LuPone.