The pool in JBoss is all handled in the DataSource configuration. Here is the HowTo. The web app would have to do a JNDI lookup for the datasource to get the database connection rather than doing a direct JDBC URL, and then you will have pooling.
Transactions are another story, though.
EDIT: In response to your comment about how this affects the code, this is what it looks like:
String jndiPath = "java:DataSourceJNDIName"; //The exact prefix here has a lot to do with clustering, etc., but if you are using one JBoss instance standalone, this works.
Context ctx = new InitialContext();
DataSource ds = (DataSource) PortableRemoteObject.narrow(ctx.lookup(jndiPath), DataSource.class);
Connection c = ds.getConnection();
Technically speaking the PortableRemoteObject.narrow isn't necessary in a JBoss (4.2.2 anyway) single server configuration for sure, but it is more proper J2EE standard code, as general application servers don't have to return an object of the right type just for doing a Context.lookup.
The above doesn't cover the resource utilization and error handling issues. You are supposed to close that Context object when you are done with it, and of course the database connection, although JBoss will yell at you if you forget to close the database connection and the transaction ends, and close it for you.
Anyway, that Connection object is usable just as much as DriverManager.getConnection(url);