Can a non-admin add Entry types into a section?
You would have to write a custom plugin that provided its own UI (outside of the Settings portion of the control panel) and that plugin's controller could mimic Craft's SectionsController (with the exception of not requiring an admin) while calling SectionsService's saveEntryType.

For security your plugin should also register a custom "canSaveEntryType" permission so you can have fine-grained control over who can call that method.