This can make a very noticeable difference for small stations. Also, the sky behind the moon can be very noisy at certain times. All planets, stars, etc. Practically all software intended for EME use includes this data. You can download Z-Track from this site, but there are several other eqaully good programs available.
Signals also tend to exhibit a rapid, almost fluttery fading known as libration fading .
Libration can cause signals to go goth above and below the average level. Libration peaks, which can last up to a couple of seconds at 2 meters, can actually help the small station make contacts they would not be able to otherwise. Another phenomenon not specifically relating to the moon which should be mentioned is ground gain . Simply put, reflections from the ground in front of an antenna cause peaks and nulls at certain elevation angles when the antenna is pointed at the horizon. In practice, it is somewhat less than that but can still make the difference between working a station and not working a station.