Most fresh water pumps nowadays are internally regulated, it'll say so in their literature.
I think it may pump water through your manual pump, as all they are is a diaphragm, and two check valves, both of them oriented in the direction of flow. You'll probably have better luck putting the electric pump between the foot pump, and your water tank, as most electric pumps tend to be better pushers than pullers. If it were me, I'd just do away with the foot pump altogether. It's simpler, Shurflo, or Jabsco, etc. are notoriously reliable pumps, and without a pump for the sink in a catastrophic failure, we're not talking about a survival at sea situation.
You may want to consider an accumulator tank as well. It will work fine without it, but it'll keep the pump from cycling on and off so much, ie:longer pump life, and less noise.
One more thing. Try and use an isolater of some sort, rubber etc. between the pump and a hard surface in the boat. You'll hear that thing every time it runs.