Sure, it's generally fine. There's no network-wide Stack Exchange rule that would prohibit this, and in particular, no rule against linking to other sites. (Individual sites may have such rules, but I don't know of any that do.) And honestly, given that you are asking the question elsewhere, most communities would probably rather have you mention that you did it than not.
However, you do need to be careful how you do your updates.
I'll update this thread to reflect any interesting answer I may receive in one of these links.
Specifically, if someone posts a good answer on another site and you want to "import" it to your question on Stack Exchange, make sure you post it as an answer. Do not edit it into your question. Also make sure you're not plagiarizing the other answer, which basically means you shouldn't copy it or quote it in its entirety; instead, use your own words to explain what the other answer says, and make sure to link to it. I'd also advise that you not "import" all the other answers you get on other sites. Just bring in the best one after some time has elapsed, and even then only if it's better than any of the answers you get on SE. It's bad etiquette to post a whole bunch of answers to your own question, and worse etiquette to engage in large-scale copying of external content.
Maybe you already knew most of that, in which case you're good. I just wanted to make sure it was clear. (Your usage of the word "thread" to refer to an SE question made me a little suspicious.)