Are modern commercial airliners flyable without operational computer systems?
For a non-fly-by-wire airliner, yes.  It's just another airplane in the end and as long as there is hydraulic power you can fly it.  If the weather is clear you don't need any electronic aids at all, if you know how to fly in the first place.  

For FBW, where computers control the controls and the pilot is just telling the computers what he wants to do, they are dependent on multiple levels of electronic redundancy to account for those sorts of breakdowns.