Sir Softaculous does not interfere with the WordPress automatic updates. By default since WordPress 3.7 minor version automatic updates is enabled in WordPress and we leave the configuration as default.
At the moment if you check to have Softaculous to Auto Update it will update minor as well as major releases when the package is updated in Softaculous. We will add the options for minor and major version options and plugins or themes options soon.
>> if auto update is NOT checked, is Softaculous somehow suppressing the native auto updater built into the WordPress core?
No we do not suppress any feature that is available in WordPress (or any other script) by default.