I've occasionally tried to meld with a vocalist provided by a client, almost always for a wedding (father sings to the daughter). Even with a rehearsal in advance, you generally find that the amateur can't hack it in the key that you are in.
If you have the luxury of a rehearsal with an impromptu singer, you can find the singer's key during the rehearsal and play the tune where the singer can sing it. Without a rehearsal, I usually spend a few minutes with the singer before the set and find the key. In a pinch I'll do it on the spot. "Sing me the first few words so I can find your key."
We were playing a big band gig at a country club in Palm Beach. They said, "We have someone here who wants to sing." It was Joni James. (Remember her?) She walked up to the bandstand, took the microphone and started singing one of her hits without telling us in advance the tune or her key. Bummer. She was singing between Eb and E. In the cracks. I hovered over the keys wondering what to do. The bass player looked at me and shook his head. He played in the cracks with her and gradually pulled her down to Eb. Then he nodded, and I came in. Later she said to me, "That was very effective how you had me sing with only the bass and then came in." The bass player just grinned.