If you just use the normal "request deletion" process, all that happens is that somebody manually suspends your account, and after 14 days (or more; 14 days is the minimum) it goes into the deletion queue. So it would take at least two weeks, but it could take much longer. (The deletion queue is kind of lazy; that keeps people who are suspended for ToS violations from developing expectations.)
If you state in your request that you want immediate deletion so that you can recreate the account, somebody with sufficient access (and there are only a small number of them) will manually initiate the deletion process on your account, and it only takes a couple of hours to complete once it's been started (it has to delete files, databases, DNS entries on the name servers, activity timer entries and so forth, so it's best to let the system handle it--nothing gets missed that way--and how long it taes to ripple through depends on what other tasks are in progress at the time).