Brian;
The VFD will always have a certain response time to a change in flow. The VFD is monitoring pressure. When a valve opens or closes the flow changes which causes the pressure to change. The VFD then has to adjust the speed of the pump until the pressure returns to the pressure setpoint. There will be large over and under pressures while the VFD plays catch up. The higher quality the PID control loop (the better written the internal VFD code) and the ability of you to properly program it can determine how well it responds.
An accumulator can help but is not a simple plug and play solution. An accumulator could be though of as a hydraulic cylinder with a spring trying to force the ram into the retracted position (the spring tries to empty the cylinder). In your case, lets say the spring applies exactly 3000psi of pressure to the ram. The problem is that if the pump outputs just over 3000psi then it will fill the accumulator. Once the accumulator is full it can not buffer sudden reductions in flow demand (there is no place for excess fluid to go). The opposite applies if the pump outputs slightly less than 3000psi. When the accumulator is empty it can not buffer sudden increases in flow demand (no excess fluid to supply).
Now, as I posted before. If you tied the VFD feedback to the accumulator and kept the accumulator 1/2 full then it might work. I have never heard or read about this being done but in theory it might work. Basically, use the VFD to keep the accumulator 1/2 full and then the accumulator will be what actually maintains the pressure.
I think you could also use a full accumulator and an over pressure relief valve, both combined to keep the pressure within some working range.
Maybe you could use 2 accumulators, say at 3100psi and 2900psi, with one taking care of pressure surges and the other taking care of pressure dips.
It also might work if the changes in flow are gradual allowing the VFD time to keep up to the pressure changes.
There is yet another issue in that a positive displacement pump likely will not allow excess pressure to dissipate. If the flow goes to 0 and the pressure spikes, the VFD and pump could drop to 0 speed and still not drop the pressure back to the setpoint.
All of these potential and application problems are solved by simply buying a variable displacement pump.
If a variable displacement pump matches the fluid pumped to the flow demand then the VFD might add a little to the efficiency but certainly not enough to make it a valid option based on possible energy savings. Despite the general image in the marketplace that any VFD installation will save energy, a VFD is often not an energy savings device.