I've broken my finger during training more than once., I didnt stop fighting till after the match was over.
In fact, training in Jiujitsu has destroyed my fingers. They are swollen and twisted and I have to wrap them with tape when I train. Part of the sport I guess.
Anyway, I wouldnt rely on breaking fingers to win a fight. You can do it in a real situation, but it wont stop someone who is trying to seriously hurt you.