To answer your question, yes it does take time to get approved in directories. Depending on how frequently they add new sites and how many other sites are waiting to be approved it can take anywhere from a day to several years to get approved. I actually just got an e-mail back last week from a site I contacted two years ago telling me they finally added my link.
The general consensus is that even if you had gotten listed in all 600 directories, you probably wouldn't see any additional traffic anyway. Google devalues those directories so much that it's almost not worth having a link there.
Thanks for reply. My site was submitted to all these directories within a week. They must have used a software to do the job, if not they would to gone bust if they were to submit it manually.
I am not sure if Google will devalue those back links because BOTW is sort of like that?
My objective is to get more exposure for my site and therefore I really hope to get 1 or 2 visitors from those directories.
Am posting my question here is also to verify my doubt that they could have taken my money and do nothing? Therefore I need to verify with you guys on their explanation that back links from web directories won't show on search.