Gents:
Mechanical back-up is rudder and trim - both need hydraulic pressure to work, so a triple hydraulic failure leaves you with NO flying controls. You have engine thrust, gear extension and passengers running forward and rearward for control ... mechanical back-up is designed to provide a minimum of control following a complete loss of electrical power (side sticks don't work!) ...before you can get the RAT deployed, and the emergency generator up to speed.)
Mechanical Backup on the Airbus is not a redundancy against hydraulic loss. It's to be used "during temporary loss of aircraft electrics" whilst the backup gen comes online (from the Airbus FCOM) and requires at least one functioning hydraulic system.
As has been said above, total loss of hydraulics on the Airbus results in loss of all flight controls.
Locked Door, could you elaborate how the A320 is still flyable after a triple hydraulic loss? I haven't found anything in my books ... A320 needs always at least one source of hydraulics to control the (remaining) flight surfaces. Lose all of them and your remaining flight time will be rather short.
Grateful for the clarification, and FWIW, this appears to match my outdated A330 systems diagrams and systems explanation. The further commentary on fuel dumping, or its absence, is also appreciated in terms of adding to understanding. (I realize this is an A320, but the similarity in design philosophy does not surprise).
Likewise, grateful for the commentary on reasons to, or not to, remain airborne while trying to recover use of one of the two hydraulic systems that had shut down. For all the bickering, there is some very good stuff in this thread.
