It is possible to deploy your Java EE to EC2. These are the probable steps:
1.    Begin by starting an instance
2.    Then Install a Java EE application server
3.    Install your application (war/ear) into the application server
These the options you have
1.you can bundle the above into an ebs ami,  
2. you can write a script (bash/tcl) which will apply these changes when your instance initiates. The scripts enables modification of what gets installed/started/moved around without having to rebundle your instance.