Possibility to use WordPress built-in localization

It is possible, and in some cases make sense, but I would advice against thinking that way. Some words in the context of wordpress core admin might be translated differently in the context of a theme.

If the motivation here is to save translation time, then don’t bother as any one with translation experience will use software that has a DB of translations and will auto translate such words. In addition common tools (poedit) are text domain blind and can not differentiate between different text domains, therefor it will be hard to not include ‘submit’ as part of the .pot file even if it is not actually needed to be translated.

Last and very least, loading the core translation is a performance hit that better to avoid if possible.