The answer is a definite YES, because Moonlight is nothing but reflected Sunlight.
Solar pv panels do convert moonlight to electricity. It can be used to power PV cells at a cost of 345:1, meaning, a panel that would normally produce 3450 W at high noon would produce only 10 W of power during the full moon.
The quarter moon (50% illumination) would likewise produce only 5 W, and so forth. Concentrating moonlight using reflective or refractive techniques would enhance the wattage.
As long as the light has a wavelength within 400-1127 nm (violet to near-infrared), the PV cell will convert it to electricity. It doesn’t matter if it is sunlight, moonlight or flashlight.
With a full moon on a cloudless night, you get about 1/350,000 th as much as at full noon sun. So your 7,000 watt solar roof might output 20 milliwatts at full moon. Your inverter might cut out at such low powers, so you might get nothing from your system, but the solar panels are producing.
A solar panel that’s rated at 50 watts produced enough current to light up a red LED (I have tried it).