No.
When the left side of the signal goes negative it hangs up on the bottom diode and will not go negative. So the right side pushes up and charges the bottom cap. Next then the left side goes positive it pushes up and charges the top cap. In one cycle you will have the peak voltage on each cap and they add to make P-P voltage.
Doesn't this assume the cap is not charged on it's cycle? Once it is the power will go through the load and through
No.
When the left side of the signal goes negative it hangs up on the bottom diode and will not go negative. So the right side pushes up and charges the bottom cap. Next then the left side goes positive it pushes up and charges the top cap. In one cycle you will have the peak voltage on each cap and they add to make P-P voltage.
LTSpice shows this as otherwise, if there's a significant load. Say the right side is positive, the upper cap charges and power goes through the load and up through the bottom capacitor.