No. The Umayyads ruled initially from Damascus (660s-750s) until
they were overthrown by the Abbassids. Abd er-Rahman re-established
the Umayyad Caliphate in Al-Andalus (Islamic Spain) in the city of
Córdoba. The Umayyads ruled from this city until the dynasty ended
(750s-1030s).
However, the Umayyads never ruled from Medina.