Yes, but too complicated.
The simplest requires two pins: one to charge and the other to discharge / adc. No diodes and no dedicated discharge / adc pins.
A better approach is to use the analog comparator:
1) discharge the capacitor.
2) charge up with the appropriate energizing pin;
3) When the comparator flips, capture the timer count -> that indicates the capacitance.
Unless you have a way to measure the internal reference, I would use an external precision voltage reference as one of the source for the comparator.
That is too complicated... WAAAY too complicated.. but typical of *dhenry*.
Build the circuit and use the internal ADC reference (1.1V) and calibrate the circuit with a known capacitor.
Better yet use (borrow) a capacitance meter and use it as the comparison standard... It can't be any worse than the measurement required to find the "Exact" value of the ADC reference voltage. The only thing important is that the reference voltage must be a constant and not vary. The rest is all number crunching.