Did some checking around, and, yup, just about everything can fly without a winglet.
Fuel and takeoff weight penalties.
I get a real kick out of news articles based on "the horror of _X_ flight operated in such an unsafe manner!"
Talk to an otherwise smart friend about a jetliner, and you'll get amazing answers.
One of my buddies thinks they have five wings -- the big ones, the two little ones, and the one that sticks straight up.