Turning off sync won't log you out, it just won't refresh the account on your device.
Most all email apps won't log you out, people use a secure screen lock for security.
However I remember others posting that there are apps that can lock other apps.
I use the Yahoo Mail app that does not rely on the Master Sync being on, and is fairly instant. It has it's downsides in regard to formatting.
Hopefully someone can advise, and remind me how to secure an app (though it may not work on the stock Samsung Email app).