No an anemone will not "nuke" your tank. That's ridiculous. They will do the same damage as an other rotting coral, nothing more. However, they are harder to care for than some corals. If you don't have the right lighting, you're going to have trouble.
I had a bubble tip in a 14G OCeanic BioCube without any issues, and when it split, I just sold the babies to my LFS.
Anemones can roam around, and there's no guarantee when you get one that it will stay there, especially if your clowns annoy it too much, like mine do. I have one bubble tip that roams all over my 155G and did it in my 40G as well, it never stung anything though. I've seen aiptasia do worse damage than a bubble tip in all honesty. It's always a risk when you add an anemone to a tank, but to answer you questions, no it won't kill your tank, and you're tank being too small is a completely subjective question unfortunately, it's personal opinion on this one.