Is it possible to have a graphic field in Database?

I am creating a database for library books. I would like to have the cover page of books to be included as one of the fields. Can the Database of LibreOffice do it?

Yes, of course Base do it!
Describe in the table field with data type Image.
Insert to the form of Image Control.
Bind it to Image data field

Yes, this is possible as described above. However, you may need to be careful because if you save images the database becomes a large file which means it either crash or load very very slowly. I would like to advice you to use links instead.

perhaps some database backends do this better than others.

No not really, at least not that I know of. As a hobby I do websites with mysql and it will probably not crash but it is still better to use links instead of the database it self. It just slows… It will cost you performance or you will need to have an very powerful server which can handle the large files (eventually it will eat your performance away).