Yes, if you choose the delete from library option, the books are removed from your library on the Kobo site. But, they will be in the trash in the library. You can restore them from there or delete them completely. When this happens depends. If WiFi is active, then it will be deleted immediately. If not, it will happen the next time you sync.
An alternative is to hide the deleted books on the device. If you select the "Only show downloaded items" options in the Library settings, these books won't show in the library lists on the device.
|