Well a diode doesn't by nature allow current to flow in both directions. So basically if it is working it is going on and off 60 times a second, spending half it's time off. When a diode is blocking the reverse bias heat dissipation would be increased. Likely shortening the life of the diode as well as producing half the light and generating excessive heat.
When forward current is applied there is a little resistance and therefore some heat is generated. When flow is reversed the diode acts as an insulator. Forward voltage drop is increased as temperature increases and therefore blocking the reverse current half the time and creating excessive heat will further degrade performance of the diode during the time voltage is flowing forward.
Honestly it's not something I have ever experimented with for the aforementioned reasons. It's just not how LED's are supposed to be implemented.