That will depend on the directory tools like Synup, Moz Local can tell you when they go up on certain sites.
If it's not a popular one there are a few different scenarios :
- Do they give you a temporary page that is only visible to you and will go live after it's approved? You can check the HTTP header response fo it and if it returns 200 it's probably approved and live.
- Do they give you a live URL that says it's pending verification? Scrape the page and use XPath to see id that bit of text changes.
- etc
Give us some more info on it and perhaps we can help.