If the radials are horizontal, the field of the radials cancels out. If the
radials are drooping, the radials radiate considerably. Is there any
advantage in either configuration? Perhaps for feedline decoupling?

The field pattern will be different between transmit and receive, because in
receive mode the radio wave can be coming from the source in any direction.
Does antenna reciprocity theorem cover this, as usually people state that
the field pattern is the same for transmit and receive?