From the current B737 Flight Crew Operating Manual:
Hydraulic panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Set P2
If pushback is needed and the nose gear steering lockout pin is not
installed:
WARNING: Do not pressurize hydraulic system A.
Unwanted tow bar movement can occur.
System A HYDRAULIC PUMP switches – OFF
Verify that the system A pump LOW PRESSURE lights are
illuminated.
System B electric HYDRAULIC PUMP switch – ON
Verify that the system B electric pump LOW PRESSURE light
is extinguished.
Verify that the brake pressure is 2,800 psi minimum.
Verify that the system B pressure is 2,800 psi minimum.
If pushback is not needed, or if pushback is needed and the nose gear
steering lockout pin is installed:
Electric HYDRAULIC PUMP switches – ON
Verify that the electric pump LOW PRESSURE lights are
extinguished.
Verify that the brake pressure is 2,800 psi minimum.
Verify that the system A and B pressures are 2,800 psi minimum.
So, in answer to your question, yes leave HYD PUMP A off.
Also when the loadsheet arrives, does the PF and PM do a loadsheet review?
The following comes under the heading of Pilot Flying and Pilot Monitoring so therefore is completed and checked by both:
Inspect Loadsheet to verify if Final or Provisional. If Provisional,
confirm final Loadsheet figures have been received and actioned as per
the Late Close Out Procedure.
Confirm vital data is set for correct runway intersection and departure,
the correct runway on ND, correct speeds set and confirm correct thrust
and derates set.