Yes, mercenaries are cost effective in conflicts, because it is worth it to them to join the war. When someone is conscripted, they might prefer to do something else. Mercenaries are generally glad to be in the war because they are being paid more to fight than they are making doing anything else. A country should just raise their prices until enough people join the army.
Maintaining security is one way to use mercenaries in a conflict as a cost-effective way to obtain mission objectives. That way, the main military force can win the war while a private security/mercenary force can maintain security in areas already won. Although such firms were widely blasted in the Iraq War, mercenaries can have certain abilities and technology that a standing army doesn't. Plus, mercenaries don't necessarily follow orders and can go behind enemy lines if need be to move beyond a security initiative.