That exact same workflow exists for Passenger. I'm not even sure you can install Rails without Rack anymore. And installing and deploying a fresh Passenger install is easier than deploying a second app on a Mongrel/Apache cluster; it is very, very easy.
I know the first time that I tried to set up Passenger with Sinatra- I had some issues, despite following tutorials. I kept having to touch some file to get it to read the new files and wasn't really working as expected. PHP just seems to run after I apt-get the php stuff and drop the files in there.