(capt flies,fo does his share)
Would guess that depends on airline, we removed that automatic transfer of control quite a few years ago.
Apart from that i would agree, main issue is to relight at least one engine, pressurization is a secondary problem. And yes, our simulators show around 2000fpm cabin rate in that case, doesn't matter if it is the classic or NG. In reality i would expect higher leak rates on most classics though.