Compared to Flash Builder -- which I'd describe as a nightmare -- IDEA is quite simple when it comes to setting up and deploying mobile(Android, iOS -- devices and simulator ), and web. It's night and day better and there's nothing that it doesn't support that I've encountered.
The Project Structure window will be your friend. You'll be able to setup certificates, provisions, and link libraries. I've only worked with one ANE -- which I put together in Java -- under IDEA and never in FB, but it fully supports them.
I had been using Eclipse for years and Flash Builder since AIR 3, so it took me a couple of days to get into IDEA initially, but once I figured it out it made all of my development needs easier.
I was naive prior thinking that FB was the only way to develop AIR Mobile outside of Flash Pro, but that's not true at all and I'm so glad I don't have to even launch that bloated-antiquated-mess now days.
They have a trial of IDEA available. It's worth looking into.