I don't see why not. Even at the height of the liquid-ban insanity (i.e., the first few weeks), I traveled with a handful of whole oranges as a way to guarantee I had some means of hydration in the event of a tarmac delay. I've heard a lot of horror stories about TSA but never one of confiscating whole fresh fruit.

Sad that we have to ask this question in today's America, but unfortunately it is a legitimate question.