Once you sync your Pages and Tracks, any modifications you make to them will also be made to their copies on all your devices.
So, if you edit the name of a Page on your phone, that change will be available through the website, on your iPad, etc.
Similarly, if you delete a Page on your phone, that delete will be made on all your devices and the Page will become inaccessible to you.
You should ONLY delete a page if you want it to be completely removed from RecordBox. There is no way to recover a Page or a Track after it has been deleted, regardless of whether it is synced.