You can do it, sure, but the rot is often more extensive inside the fruit than it appears from the outside.

Yes, ripening fruit can certainly develop rot. I dip my stone fruit after picking into water with peroxide added. I don't know how much it helps, though.

I got distracted with all my deer and squirrels and the brown rot again got out of control in the last few weeks. I routinely eat parts of fruit that are rotted; if its over half rotted there is often not much to eat. If you are getting lots of rot on a tree it usually means you will get lots of rot on the unblemished fruit as they ripen inside. Rotting varies a lot from variety to variety; I have replaced all of my most severely rotting peach varieties with more resistant ones.

Scott

I just came across the following a few days ago and it stuck in my head (regrettably). The picture isn't very appetizing- I can't imagine doing that outside of a survival situation.

About halfway down the page:
"brown rot isn't at all poisonous and I often crush an affected apple in my hand (they are semi-liquefied inside) and drink the juice, which is turning into cider"