Does a stock email app auto-update?
There is a global Auto Update option in Android 7.0 (possibly previous versions but I can't check now) which automatically updates all apps.

There is also a per-application setting. In case you have the global option off, then you can have that one enabled and it will still auto update. So be sure that both are off if you want the app not to auto-update.

By default, I believe the global option is on but that might depend on the phone.

For clarity, when an app is updated, we call that an update, when its data is updated, we call that a sync, such as downloading new emails as they arrive.

Stock apps are part of the system, so they will update when you accept a system update.