Given the track record of software 'spitting out HTML' I'd be wary of anything that could claim to do the above.
Note that HTML5, by itself, doesn't make an app. It'd still have to be compiled into an app (ignoring the ability to run local web sites--which I assume isn't what you are talking about).
As such, you likely need to get this all into PhoneGap at some point so the HTML5 can be compiled.
Before doing any of that, though, I'd take a look at Apple's new eBook authoring software:
Which was designed specifically for creating interactive eBooks.
After reading more of your comments, I think what you are really looking for is a way to create a self contained HTML 5 app. There are two ways to handle that:
1) create a web site with a manifest file and implement local storage. That allows a user to download your site and store it locally on their device.
2) Use phonegap to create an App from your HTML5.
Option 1 is slick, but rarely used for a number of reasons...the big ones is that people don't really know you can do that and it makes it hard to create a paywall.
Option 2 is not too hard, though I don't think InDesign will help in any way. You basically just build your HTML5 site as you see fit (animations would be CSS or Canvas) and then compile it into apps for each platform.
The reason I mentioned iBook Author is that it's an authoring tool, akin to InDesign. So that's a solution coming at it from the authoring standpoint more than it is on the distribution end.