Can I use a dusk to dawn LED bulb in the hanging light?

Technically yes, but practically maybe not. So long as your dusk to dawn LED bulb is an E26 base and draws less than 60-watts it should be possible. However, note that the bulb will be enclosed in the lantern, and its sensor may be impeded by the glass lens, the fixture body, and possibly the overhanging canopy.

So try it out, but most likely the D2D bulb is not going to work properly with this or any hanging outdoor light.