There's no inspection. My arcs usually appear about one minute after I hit the publish button.
There is a bit of a lag time between when you submit it and when it shows up on your personal published list but if you search you should be able to find it.
Check the AE chat channel as it will let you know when the publish is completed. For me it runs about 20-30 seconds for a 99.3% full arc.
I have noticed that most of the time when I'm awarded a badge for publishing a mission, that it doesn't publish, and I have to hit the publish button a second time.
And before someone comments on that, yes, I have checked to make sure it was not published twice.
@Doctor Gemini
Arc #271637 - Welcome to M.A.G.I. - An alternative first story arc for magic origin heroes. At Hero Registration you heard the jokes about Azuria always losing things. When she loses the entire M.A.G.I. vault, you are chosen to find it.
I submitted a mission last night, about how long does it take the devs to process and inspect a mission before it shows up in the list for other players?