Yes, I play without nails, and have done so for over twenty years. I have a website half devoted to playing without nails, half to my performances and other things: http://rmClassicalGuitar.com
You will find a Players page, with a list of players passed and present who played without nails, many of whom made recordings, and quite a few who are still active today. The styles run from Romantic through to avante-garde.
I interviewed Virginia Lucque about her technique - which is formidable! - wherein she revealed that it was indeed Segovia who gave her some tips on how some players used to do it. For some it involved growing the nail a little so that it adds strength to the flesh, yet not long enough to reach the string. The difference between not long enough and too long is very short, so needs daily attention. Not all flesh players adopt this technique, I certainly don't.
Anyway, lots more info on the website.