I would agree that Calvinism is a description of how people get saved rather than "the gospel itself." It isn't necessary to understand the "technical schematics" in order for them to be effective. The gospel is the message about Jesus and His work on behalf of sinners, not the tech manual on how He did it and how the process works from start to finish.

<font size="4">However:</font>

No one can seek His aid without admitting one's need for aid (thus Holy Spirit "teaching T," if you will), and no one comes to the Father unless the Father draws him (no one can), and no one hears without having his ears opened (because we were dead - not just "sick" - in trespasses and sins), and no one calls Jesus Lord except by the Holy Spirit.