The accumulator plays no part in system operation while running. its purpose is to maintain pressure after the pump has stopped.
If the car is running badly testing must be done. As to fuel pressure, it's only requirement is that it stay constant and within bounds. This is really an either/or situation: if fuel pressure is maintained thats all thats necessary from that standpoint.
If a car is running bad the first question I ask is whether the condition is the result of single cylinder misfires or whether the problem is systematic. With experience a good tech will usually determine this by the seat of his pants.
Individual misfires are identified by scope analysis or cylinder balance testing. Systematic problems (mixture too lean/rich, timing too high/low, etc.) are usually dealt with by either substitution or evaluation. By substitution I mean by changing the status quo and seeing the results. The easy one is mixture. I remove the aircleaner and lightly press on the airflow plate. If the car runs better then the car is running too lean. One can usually grab the plate by the 10mm nut and gently pull up to lean up a mixture.
Much of this is done in a few minutes by a driveability tech to determine which tooling to use for real evaluation...
Bosch Master, ASE Master, L1
33 years MB technician