This is a loaded question and I suspect most will adamently say they
would not! However, it isn't too hard to come up with a number of
scenarios in which a pilot would take off with known "legal" problems
that are not affecting safety of flight, and some which are mechanical
problems that do affect safe flight in a very personal manner.
Now I am going to sit back and watch the weekend pilots take their
best shots, and hope to see some pros who have been out in the bush
and had to make the hard decision as to take off or sit and wait for
help.
In years past, I have had to do some flying that I probably would have
fired pilots over if they were flying off concrete and wearing ties
and white shirts.
Like I said, this is a trick question and meant to stir the pot to
create some very real day to day scenarios.
Ol Shy & Bashful

This happens every day all over the country in all types of aircraft. It's
part of the pilot's decision process. I've ferried planes where one of us
flew and the other guy was under the panel making repairs while the pilot
held the flashlight for him.