If I do an intrigue challenge and my only participating characters strength is reduced to zero. Can I still win the challenge with my Master of Whispers title?

yes. it provides +3 STR to the challenge, so you still have 3 in the challenge (as long as it wasn't a kill/discard if 0 effect). If that's enough to win, you win.

As a note, even with the title, if they kill all your attackers/defenders, then you have nothing contributing to the challenge and either they win if they have participators or it's nullified if they don't