If the site is not eligible for a listing in DMOZ, then never. That's no different to any other website that offers non-recip links for sites that meet specific criteria.
If the site is eligible for a listing, then just as fast as the volunteer editors can get to it.
Very, very roughly, there are an estimated (and estimates vary widely) 5,000,000 sites today that are eligible but not listed.
Slightly less roughly, something like 2,000 new sites are added a day.
That leads to a raw average of about 3.5 years.
Raw, but meaningless. It's a bit like deciding whether you need an umbrella today based on the world's average rainfall:
Analyze a year ot two's ODP RDF download files and you'll spot very many interesting "weather" patterns in the listings and delistings rate across many categories.
True, historical data is only a guide for the future, but it's as close to a "realistic time frame" as possible. Let us know what you find.