Thank you all for your help. I had indeed not understood the notion of 'free pages' which affected the way to retrieve the actual number of used pages.
And indeed, with recent versions of OpenLDAP, I noted that it was possible to retrieve this information by querying the monitor database (attributes olmMDBPagesMax, olmMDBPagesUsed & olmMDBPagesFree for those wondering).
@Clément: I also implemented a similar monitoring plugin :) (https://exchange.icinga.com/brenard/check_mdb). Don't forget to share your works on this great website (and possibly on https://exchange.nagios.org) ;)