I have the latest iOS app from the store on my iPhone 5 w/ iOS 7.1.1 device. When I launched it this morning when pretty much all of SE was offline, it crashed silently. This post seems to indicate that that app works in read-only mode, but that didn't happen for me. When the sites came back online, the app behaved as normal.
If it matters, I was already logged in via Google, and I am pretty sure I had pending notifications in my inbox (I think this is why I open the app).