Oh yeah, it does.
As for Diavolo's and Trish's souls being identical to Bucciarati, that's the one thing I actually won't call bullshit on. They are closely related, and Trish can sense Diavolo's presence, so it makes sense that their souls are very similar or identical. In any case, it seems souls and bloodlust are separate, since Diavolo's bloodlust only made itself apparent when Polnareff showed up, but not before then.