Accumulator? in one word..No.
The accumulator only holds the working pressure in the system until you go to start it,so the engine doesn't have to crank over and wait for the pump to build pressure.
These engines are Known for Clogging the intake ports. A dealer will have the equipment and know how to clear the ports which may be closed up enough to do what you describe.
The cheaper alternative is to seek out a Carboclean franchiser *and get them to run over your car with their machine.
In the mean time get the mechanic to Double check his work on the cam timing,it only takes a few minutes to remove the cam covers,turn the engine until the cam marks line up and read off the crank shaft timing mark to ensure it's all within spec.
*http://www.hilltopmechanics.com/carbonclean.html