What the heck, let's calculate it!
Per Wikipedia: the geostationary orbit radius is: 26,199 mi; Earth's radius is: 3,963 mi
The angular diameter of the Earth from the satellite should be: 2 x arcsin(1/2 x 3,963 / 26,199) = 8.675 degrees,
or if we measure from the center to the edge: 4.337 degrees
Moon's orbit inclination is about 5.1 degrees - which means, if I am correct in my calculations, it should stay within 4.337 degrees of the equator, most of the time!
So, it should be passing behind the Earth within our view most of the days! About once every day for a few days in a row around the day when the Moon crosses the equator, which happens every 2 weeks or so.
However, we also need to take into account the location of the Sun: on some days the Moon may not be visible, simply because of the bright sunlight shooting straight into the lens.