I read this thread title wrong, too. Except I thought it said "Would you date a friend of a relative?" And I was about to jump in with both feet and say NEVER AGAIN! (You just have to know about the types of friends that my relatives have, LOL.)
But in answer to the original question, I think it would depend mostly on the people involved. Some friends/friends' relatives are mature enough to handle the situation and some aren't.
When I was in graduate school I went on a date with my Diamond sister's older brother!! He was a hottie! But things didn't work out because he was moving...but we kept in touch over the phone for a while....but it did not change me and my diamond's- who was also my best friend- friendship!
I ended up hanging out with my friend's cousin last night. We had a good time and he said he was glad she introduced us, and we both feel that it was one of those things where we just met, not really to be "set up" by her.