It is Harville telling the story, and I think that he thinks that Capt. Wentworth saved Benwick from suicide, from his phrasing.

Whether Capt. Wentworth really did or not, I would more likely believe coming from one of the two gentlemen who were there. But, given probabilities, Anne is unlikely to hear the tale from either. I think we are left with only Harville's opinion, and our own guesswork.

In my opinion, Benwick might have suicided, or done something reckless that might have cost him his life, immediately after hearing the news, but he is unlikely to have done so after the first shock was over.