Can I use Connection.isClosed() to validate a Connection?

No. Here's the quote from 2.1.9 Freeing DBMS Resources:

"Note that the method Connection.isClosed is guaranteed to return true only when it is called after the method Connection.close has been called. As a result, a programmer cannot depend on this method to indicate whether a connection is valid or not. Instead, a typical JDBC client can determine that a connection is invalid by catching the exception that is thrown when a JDBC operation is attempted."