I actually do it pretty often! Sometimes google on laptop, pull up the words and chords and take off.
I did it Thursday night. Hate to tell you what the song was, but I will. . . Blanket On The Ground. It was good enough for ten bucks! Didn't sound much like Billie Jo Spears though. More like Waylon, and he's been dead a while now!
Occasionally I will realize I'm in trouble and just turn it into an instrumental, but if I really haven't heard the song or it seems too hard, I will skip it and maybe play an MP3 of it from Youtube when I take a break.
When I get one of these requests, if I like the song at all I will make a point to write down words and chords and learn it for "next time".