IMHO, yes. It would improve content discovery, which becomes more of a problem as a forum like this
scales in users and content speed. Lobste.rs has them no one seems to mind, so I don't think an argument could be made that tags per se would negatively affect quality. Similar stories can be cross-tagged by the mods, and only the latest (or most popular) could appear on the front page, acting as flood control. And, Hacker News already basically has tags with Show HN, Tell HN, Ask HN.
A more interesting question might be, how hard would implementing tags be in HN, given that it doesn't use a database?