And the answers are Yes, I mentioned the possibility of different sender resistance and it probably won't matter - our circuit is just averaging a varying voltage and doesn't care what that voltage is.
Once the cap charges to whatever voltage the sender defines, the cap acts like an open circuit, floating at whatever voltage it sees from the sender wire.
As the gas float drops, the voltage level in the circuit changes (could be up, or down, depending on the gauge and sender design). The cap will resist this change by absorbing voltage or adding voltage to the circuit, depending on swing direction. The resistor slows down how fast that happens. By varying the resistor and cap values, you can change the charge/discharge time, and vary how quickly the needle stabilizes. When the float stops moving, the cap charges to that sender voltage and sits there.
I haven't tested this yet, but this should also cause a slower swing from zero to the current fuel level when the ignition is first turned on. Same thing when you fill the tank. 2 - 3 seconds or so, just like our old Honda gas gauge.