Anything has it's limit and by saying that, BTCitcoin is no exception to that as well so there's a point where it could be classified as fragile too but the chances of it to happen is a lot lesser than fiat. One of the things that could make BTCitcoin fragile is it's users and the way they decide to do with BTCitcoin so aside from this yes, BTCitcoin could somehow be anti fragile if those risks are eliminated.
It could be interesting to classify gold first - and bitcoin comes more or less the same - if its tech stuff is all solvable.