If it was accepted you can see the website listed in the directory.
There is no way to know if a website is rejected. But you can check if the website meets the guidelines http://www.dmoz.org/guidelines/include.html
If the website is not a type as listed in "Sites Generally Not to Include" than it is either lsited or still waiting review.
Time between suggestion and review can vary between a few days and several years.
This site has been archived and is no longer accepting new content.