A MOSFET gate looks like a capacitor that must be charged and discharged. The memory, if you can call it that, disappears quite rapidly in relative terms. It is similar to a series RC circuit where the voltage rises and falls exponentially with a time constant τ. As a rule of thumb, it takes about 5 time constants to reach 99% of the final value. I would not expect any "summing" action on MOSFET gates.
That said, a schematic diagram of what you have in mind is worth more than several paragraphs of verbiage and maybe I don't understand what you are describing.