So I guess this is for Windows as you mention an exe?
I don’t know much about Adobe Air, other than the few apps I have tried have required runtimes to be downloaded directly from Adobe. One problem with Air, AFAIK, is that you can’t distribute it yourself, so your users are taken out of your app to get the Air files required to run your app, so you distribute the application files, but the runtimes from Adobe are required to run your app first - this may have changed from what I remember, it was many years ago. This may not be the image you wish to portray to your users.
One possible solution, would be to have a look at SWF Studio, from Northcode . You will need to know some Flash or Flex, but you can use SWF Studio to embed a browser, and any required files that can be packaged into the exe, and then extracted at your convenience. Taking it a step or two further, you might also be able to embed your complete rails app, which may not be what you want anyway, but could be an option.
The guys at Northcode are old school programmers and extremely helpful. You can download an unlimited free trial which will build your exe with a 24hr expiration period, so you can build and test an unlimited number of times before you decide to purchase.