You're right.. this IS an AMA thread. Any questions asked, even if already answered somewhere in these 1400+ pages, are acceptable people!
So to answer your question, as 'digression' already mentioned.. the timelines vary widely from a few days to a month plus..
My personal experience (5 years ago) was I completed the GAT, they told me I passed on the spot, and then I got a phone call about a week later asking me to come in for an interview.
Others here have waited much longer. So it varies... Good luck!