Just curious as to whether this has ever happened, and if so, what the result was -- spammy answers, or increased engagement and new traffic?
I don't think we've had any hot network questions on Sustainability SE, but I admittedly I'm not sure. The problem is that there is no way to search for questions that were once a hot network question (HNQ) or check if an individual question has been HNQ (feature request for that is on Meta SE). Moderators can check if a particular question was a HNQ in the past, but not search for such questions.
The only experience I've had with this is when a question I asked on Politics SE became hot (it's this question). I asked it in the morning and received 2 answers. During the day it apparently became a hot network question and it started receiving quite a lot of views and upvotes in a short time. I earned both the 'notable question' and 'good question' badge within a few hours. One more answer was added while it was 'hot' and several comments were made on the answers, but that's about it.
Update Aug 21, 2019: I noticed that this question has received a lot of views in a very short time. Further investigation shows that it was marked as a hot network question about 19 hours ago. When hovering on the question in the HNQ-list a pop-up is shown that says "This question has been arbitrarily awarded 7.184 hotness points". I think it's safe to say that the result is more views (2K in 1 day) and more upvotes on both the question and answers (question has 9 upvotes now, the 2 answers have 11 and 5 upvotes),
Update Nov 20, 2019: It is now possible to search for HNQs, see Glorfindel's answer
was marked "hot" one hour ago.