No, though there's such a thing as bringing about your own death, possibly at the hands of others. What I'm suggesting is that Jack becomes increasingly more unhappy and reckless, allowing his sexual preferences to become known in a place where they will almost certainly attract disapproval and maybe violence, rather than remaining discreet and appearing as much as possible and as he's done for years a regular guy, working in the family business, with a wife and son, hobby his occasional fishing trips, all from the outside quite acceptable.
Randall is a risk in a way the Mexican prostiture wasn't, just because he's local,knows the same people as Jack and the Newsomes do, and if he and Jack spend time together is liable as Jack is to be recognized and talked about. Jack has apparently avoided such entanglements with people from his own area up till now; is it because he's so miserable about the situation with Ennis that he takes the risk of Randall and the risk of being found out, with all that may imply?