Are calls made by third-party apps logged?
If you mean logged by your phone company then yes any calls that go over their network will be logged and billed to you. If the 3rd party app uses VoIP or something similar they won't log it as a call but then you also won't be billed for it except for the data charges.

If you mean logged on your phone so you can check it in the call history then that depends on the application as it is possible for an app to edit your call history.