Whether you get in quickly to DMOZ depends on whether your specific sub-category has an active editor or if it's being handled by the editor of a higher-level category as part of many different sections... and what mood the editor is in on the day he/she gets your request... and how many requests are pending in the queue... and whether the other submissions are for the most party spammy and low-quality (could be good or bad -- either yours stands out by contrast or accidentally gets tarred with the same brush)... and the phase of the moon... and what the editor had for breakfast... and who makes it to the finals of American Idol this year...
In other words, there are a zillion different factors that go into it. Having a non-spammy, well-written, properly categorized submission for a high quality, legitimate-appearing website definitely HELPS, but it's no guarantee of quick acceptance. (Mainly because nothing
is a guarantee
of quick acceptance with DMOZ.)
It's a good directory link, but doesn't carry any special weight with the search engines these days. It's just a link like any other link, and not even one of the most powerful links out there, at that. Do your best to create a quality submission, then move on. If you get in, great. If you don't, it's far from the end of the world.