The only thing on Stack Overflow that might not be public forever is a comment. If you edit an answer or question all past versions are still available. Deleted questions and answers are still visible to mods as well as any user with enough rep. Even the chat sites retain permanent public transcripts. It's possible that you could have an admin actually remove something from the revision history, but I'm not 100% sure. In short, you should assume that anything you ever post to stackoverflow has permanently become public knowledge. So in this case, yes, change your client secret.
In general, if you were to post a secret to a public place for a brief period of time, only you can decide whether or not the "cost" of changing it outweighs the risk of someone using it. If the client secret protects something low-risk (imagine a Google maps API key that is only authorized for use from your server IP), then you may reasonably decide not to change it.
Personally though, unless the key is nearly impossible to change, I would change it no matter how short the exposure.