Is it possible to query value of SQLNET.EXPIRE_TIME parameter?
No, it can't be queried. These values are stored in sqlnet.ora on either or both of the client and the server.

In either case, none of the contents of the network configuration files sqlnet.ora, tnsnames.ora, listener.ora etc (eg protocol.ora, snmp.ora, cman.ora) can be queried.

If you really need to read the contents of these files and can't solve this problem in some other way (programatically via some OS level program or even administratively), you could read the file via external tables or via a Java stored procedure.

I would prefer to solve this outside of the database.