re: OT mechanics: correlation between weak battery and engine performance paramaters

It would be nice to know what year vehicle you are talking about and what "high mileage" is.

But yes, low voltage or voltage drop under load can cause a myriad of problems with modern vehicles.

Also, it may be a lambda sensor on its way out. IE the battery was only a little bit out of voltage spec but the sensor only operated well at higher voltages.

Additionally, removing the battery can reset the ECU and cause it to relearn the operating parameters and change mixture accordingly.