A good show on Foxtel now - Flying Heavy Metal - says the opposite. Watched an episode yesterday about a simulated flight with complete loss of rudder and ailerons. With an older plane this is certain death. With the latest automation and software the plane can be flown and landed almost normally using just flaps and trim controls.
Well, if you take it a step further, the older 'fly by hydraulics' aircraft can actually be flown without any hydraulics at all, if the right software boxes are installed. They use the engines for roll and pitch control. This was tested on an MD11 by NASA, but was never installed in any operational aircraft.
But, looking at the scenario you offer...no modern airliner offers a way around that problem using the automatics. But, you would still have normal pitch control, and roll control would be available via differential power. Actually a nicer situation than some cases in which landings, with varying degrees of success, have been made.
But, what I was referring to was the habit of some systems to drop you back into degraded modes, and reduced instrument capability, with only a little bit of a push. For instance, in a 747, as it isn't a fly by wire aircraft, it is always flying in what amounts to the Airbus 'direct law'. The autopilot works, and so does the flight director. But, if an Airbus degrades enough to drop you back to alternate law II, or to direct law, not only does the autopilot cease working, but so too does the autothrottle and the flight director.
Lose two systems (for instance two air data computers) in a jumbo, and you will have lost your ability to have the pilots on different data sources, but you will be able to select them both to the same source, so they will at least have some data displayed. Autopilots, flight directors, and autothrottle will still work, though you will get a warning to ensure that you realise you are both on the same data. Lose the same two ADCs in an Airbus, and the aircraft will revert to alternate law, lose the autopilots, flight directors, and autothrust. And worst of all, depending upon just which ADCs you have lost, either the captain or the FO will lose all primary instrumentation.
My point is though, that a relatively minor failure can have downstream effects that make life a lot harder...and the automatics will never help you there, as they will give up the ghost at the first opportunity.