You absolutely do need 2x20µF to get 10µF and both capacitors contribute.
The first time you charge them, the forward biased capacitor charges like a normal 20µF cap and the reverse biased capacitor breaks down and conducts like a diode with a minor voltage drop.
When you then discharge, the first cap will be discharging and the other will be charging in reverse polarity. So from now on, they behave as a normal series combination of 2 capacitors.
This state only changes when you apply a voltage higher than any previously applied, in any direction. Or when leakage discharges them.
I had to think about that for a few minutes, and under the situation you describe, you're right--on steady state AC, assuming negligible losses, both capacitors should maintain a correct positive bias that goes to Vp for one and zero for the other, alternatively. So their 'rest' state is equally charged, but in opposition to each other. However, below 1 to 1.5 volts per capacitor, the breakdown doesn't occur and the reverse-biased cap just works like a normal cap--which also results in a total capacitance of half the individual values. In this case, the capacitor charges are aligned, not in opposition. So what happens if you gradually increase the voltage through this transition?
This transition would be right in the range of audio amplifier outputs, one very common place for NP caps, as quiet music might be well under 1 volt but almost any system can exceed 5 volts if you turn it up. I've wondered about the linearity of NP caps and many people swap them out now for various non-electrolytic types like the one I posted. However, an audio engineer once told me that they measured the distortion with NP caps and it really was pretty low. Actual NP caps are a single unit that has two oxide layers instead of one, in opposed polarity. I've always assumed that this was superior to the back-to-back arrangement we're discussing, but now I'm not sure. I have to repair some audio equipment next month so perhaps I'll do some experiments.