Yes, you can do that if you route the request/response through your Rails app.
E.g. in your index action, make a Net::HTTP request to your external site, gsub the response's body to your heart's content, then send the end result to the browser.
If you want the user to be able to navigate around the external site, you'll have to rewrite all the hyperlinks so that they point back to your own action, with the real path stored in a param somewhere, so your action can make another HTTP request to the appropriate part of the external site, gsub the response's body (including hyperlinks) and send the result to the browser.
Regards, Andy Stewart