Pumping into a reservoir isn't a very good idea. Unless you keep the completely cylinder filled, the air gap will break your pumps pressure and you lose a decent amount of flow past the res if your lucky. Most likely, and mathematically, you will lose all flow.
Fluid dynamics for your current system works like this. You have a sealed loop, with a res (with air gap), pump, and rest of loop. This works because your pump can push all the water to the air gap (reservoir). Once it hits this gap, the pump no longer is delivering any flow (pressure = zero in res) Your pump then sits beneath/after this gap (as it is fed by the res.). It is essentially submerged, so water doesn't have to be pushed into the pump. As long as it is submerged, it can pull the water in it needs. Gravity and suction head (very weak) are what achieve this.
The Bernoulli equation can be used to calculate this effect. Essentially the math states the pressure returns to zero in the reservoir as mentioned. Zero pressure means zero force. Zero force means your pump is achieving zero flow through that component. It is taking the ~zero velocity water and re pressurizing it,thus giving it the ability to flow again. You have no pump after the second res, so you have no ability to restore flow.
A reservoir after your pump means you have another air gap right after your pump. That means your pump cannot pump past it. The only way to pump past this would be to keep the tube reservoir COMPLETELY filled. So you would have a res, but you would basically be treating it as a large diameter tube instead of a traditional reservoir.
If you want two reservoirs without two pumps, your best bet is to put the pump on the bottom of the second res, with the second res completely airfree. That way gravity and suction head can pull the water it needs from the first res which acts to trap your excess air in addition to holding water. Your second reservoir again would just become a large diameter tube.
You will not see any temperature improvement as the volume of water is too small to make a difference. Your temps may appear slightly better until your loop heats up. Once it does, your back to where you started. So you gain a few minutes at best of marginally improved temperatures. More water does not equal more cooling. More cooling comes from heat transfer out of the system. Heat transfer out of the system is almost completely done by the radiator. Tube and res heat losses are marginal. Unless you REALLY like the way it looks and are willing to move your pump, do not do this. You are throwing money away for no cooling improvement.