Given your apps are developed using
Java 5 and all app servers are backward compatible hence the java version shouldn't be a problem.
JEE side (ejb) again shouldn't be a problem
As for struts or other frameworks/ libraries, I expect if you have all those jars included in the WAR/EAR, your app will run.
However, server configuration like
JDBC connection pool, JMS queue/topic, etc will need to be set up in Glassfish v4.
At the end, you just can't take advantage of those "new features" in JEE7