Does the prayer of saluting the mosque (Tahiyyat al-Masjid) suffice for the regular supererogatory (Ratibah) prayer?

Greeting the mosque (Tahiyat al-Masjid) does not suffice for the regular Sunnah prayers (Rawatib), nor for other non-regular Sunnah prayers. However, a Sunnah prayer or a Fard (obligatory) prayer does suffice for greeting the mosque, because the purpose is for the person entering the mosque to begin with prayer, and that purpose is achieved by performing either a Sunnah or a Fard prayer.