I'm not sure. Off of the feature list, it looks like a framework, not a component library. It takes over your app structure, build process, etc etc.
Other than that, aside from needing some sort of compilation step for the JSX (our demo project uses browserify and gulp) the rest is up to you.
I haven't used Om or Reagent yet but I don't think there'd be anything preventing them from working with Touchstone.
Edit: ok I found the createApp mixin and I can see you're doing a lot of stuff in there to support the touchstone app... It would be sweet if you could delegate some of that heavy lifting and integrate with react-router at the same time...
The paradigm of links and parameters falls short, and eventually TouchstoneJS will exert a lot more control over the transitions. Right now we're using CSSTransitionGroup, but I expect we'll move to a JS-based transition method (possibly with tween-state) so you can do controlled or partial transitions (required for things like drawers or swipe-from-left to go back)
We have spent a lot of time looking at react-router though, and are using it on other projects, and are / will be borrowing quite a few things :)
https://github.com/Thinkmill/touchstone-starter/tree/master/...
You should be able to piece together the UI parts you need. The starter also happens to include the build process run browserify and create a phonegap build, that's all.
(disclaimer - I might be totally wrong)