Almost all of the actual scientific behavioral and physiological studies/evidence say...no, the moon phase and light have no effects.

However...the barometric pressure, relative humidity, temperature, amount of light, wind, and even ambient noise (such as squirrel chatter and songbirds) have been recorded as having an "effect" on gobbling activity...

BUT...the moon does affect the tides, which can affect precipitation and winds...so...

I'll just shut up and go to bed, tomorrow is finally my opening day, and I could care less about tonight's moon phase...