There's no such thing as Adobe EC2, unless you're referring to the Adobe media server you can set up on EC2. But I'm assuming you're simply referring to the Amazon Web Services EC2 cloud computing service. In which case: yes, you can run a backend server for your mobile app on EC2 (and Google App Engine, too). All you have to do is write a web service that accepts requests from your mobile app, queries the database and applies whatever logic you need it to apply, and send back the data to your mobile app. But it sounds like you may want to read up on web services and cloud computing first, or this will be a rather daunting task :)
If you're not expecting too many users then simply putting a PHP script or something on a "traditional" shared server with your web hosting provider may be much more worthwhile than running a dedicated EC2 instance for your app, though.
