A typical gain pattern for a quarter wave ground plane antenna is:
For a situation where the signals of interest are below the antenna in elevation (e.g. antenna on a hill/mountain), would mounting the antenna upside down make any difference?
A naive response would be that the antenna's pattern would be unaffected except to be rotated 180 degrees, i.e.:
An answer to a similar question seems to imply that the radials on a ground plane antenna don't have as much to do with the pattern as the actual earth. My trials at modeling this with EZNEC resulted in no change based on the antenna's orientation, but I don't trust myself.
Also, looking at just the plots would lead you to believe that there is zero chance of receiving a signal from below the antenna's elevations. Which also is hard to believe.
Searching the internet resulted in many variations of "Try it." or "It worked for me back in ...". I'm looking for more specific reasoning.
And in case it matters much for this answer, I am mainly considering the 2m range of frequencies. Also for consideration, height above ground can be assumed to be in the 5 meter range.
Simplified configuration for clarity: