Noises are most difficult to describe and interpret.
The first impression can be worth something so I will give it. The noise, does it sound the same as the pump noise when locking the doors? I'm not sure but the later cars have a vacuum manifold that maintains vacuum for the A/C controls. Under engine loading vacuum is maintained if necessary by the door lock pump (PSE). These have been known to leak (and any vacuum leak might act the same way), which could cause the pump to be turned on after a period of low vacuum acceleration. It could also affect the door locks and possibly play a part in the mixture adapting poorly and causing hard starting.
That may be the length I can dream of a connecting senario.
Bosch Master, ASE Master, L1
33 years MB technician