If an aquifer is under confined conditions and you over-pump for a short time and then lower your pumping rate to allow the well to recover, do you need field parameters since the water in the screen would have to be formation water?

It really comes down to this: I am more comfortable in knowing the field parameters than not knowing them. But I can see the logic in your question, where arguably the water that you are sampling has to be from the formation.  Depending on permits or state regulatory guidance, field parameters may be required, and it's best to know you have stabilized indicator parameters.