I've called a few of those. One reminded me of someone's exasperated mom who got dragged out of the shower: "Are you shot in the head? Are you bleeding out? No? Then why the FUCK did you call me?!" I called one of the newer ones this summer, and I could have sworn the hotline worker had fallen asleep at points. Looooooooong awkward pauses. Maybe that's the next step beyond "not judging"—"offering no input whatsoever." Most of the time it's just someone triaging you for the hospital, which I guess is useful. Saves you a trip to the ER if you're not the sort of case they would admit. (Although let's be honest: nearly anybody can be the kind of case a hospital does or doesn't admit if you know the Magic Hospital Words.)
So yeah ... I don't think I've ever had a hotline actually not pick up on me, but I haven't found them very helpful all the same.