It's worth dispelling that for any 737 NG pilots. This from the FCTM
Just to add to that, Boeing seems to be quite clear with specific guidance of a loss of thrust from both engines, that prompt action is necessary regardless of airspeed or altitude in order to capitalize on high engine RPM.
And pressurisation loss should not be a factor
I think one should expect the cabin to climb at around 1500fpm. So not an immediate concern and I certainly would not delay a restart attempt to deal the pressurisation. But the cabin altitude situation probably will need some management soon, preferably after the initial start attempts.