Does Using Benzoyl Peroxide/salicylic Acid Forever Make Acne Go Away Forever?

Benzoyl Peroxide is a strong chemical that is more concentrated than salicylic acid, so you should not be using benzoyl on a regular basis because it leads to peeling and severe dry skin. In regards to your question, yes it controls the acne to stabilize its production by drying skin to control the oil & bacteria (which causes acne). Although, acne is also genetic. You can't control it all the time because it comes with puberty and your genes.
But products containing these chemicals will at least control it better.
Use Biore ice cleanser. I use it and my skin has never been clearer because it has salicylic acid and its daily usage really smoothes and clears skin, while its cooling effect really refreshes the face on a hot day.