Forum Moderators: open
First off, don't depend on the ODP for the only link by which Google might find the site. Depending on category, size of the queue, how active the editor is, an ODP listing can take from one to two days to several months. Try to get other incoming links.
According to Google's Matt Cutts Google does spider sites submitted through its add url [google.com]. This might get a site initially listed but to stay in the index you will still need to get more incoming links.
As for how long, the somewhat generally accepted time frame was two to three Google update cycles to be solidly included in the index. However, with all the brouhaha over the?current/last/still-in-the-works? update (see WebGuerilla's understanding update Dominic [webmasterworld.com]), I'm not sure if anybody can say this still holds true but that's a good a time frame as any until proven different.
Jim