Here are a few transit simulations of Earth-like planets with and without moons (Figures 1-3) including Avatar's Pandora (Figure 4). All simulations assume long cadence observations (every 29.4 minutes) by the Kepler telescope and are stellar limb corrected. They were done with SPHERE-SIM, a software tool of the SPHERE Project to simulate complex transit events for statistical studies, such as those caused by multiple stars/planets, moons, and rings.
Figure 1. Animated simulation of the transit of Earth around the Sun as it will appear from far away to a Kepler-like telescope. The solid line is the expected stellar flux and the dots are the observed values, assuming a 40 ppm combined noise. Time is with respect of mid-transit. This simulation does not include the Moon. A MP4 movie version of this animation is also available.
Figure 2. Simulated stellar flux of the transit around the Sun of Earth alone (top) and Earth with the Moon (bottom) as it will appear from far away to a Kepler-like telescope. The blue curve is the expected flux and the red dots the observed flux, assuming a combined noise of 60 ppm. The presence of the Moon (at its maximum separation of 60 Earth radii) causes a small dent (starting at -10 hours) in the expected flux but this is not apparent in the observed flux.
Figure 3. Simulated stellar flux of the transit of Kepler-22 b alone (top) and with a hypothetical one third size moon (bottom). The blue curve is the expected flux and the red dots the observed flux, assuming a combined noise of 60 ppm. Even that the hypothetical moon (located at 20 Kepler-22 b radii) is a little larger than Mars (0.6 Earth radii) its presence is not easily notable in the observed flux.
Figure 4. Transit simulation of the fictional planet Polyphemus and its moon Pandora from the sci-fi movie Avatar. This is an example of a transit of a Saturn-size planet with a Venus-size moon around a Sun-like star. The relative size of the star, planet, and moon are shown in the top frame. The presence of a moon (bottom) is barely notable (starting around -20 hours) against the strong transit signal of the planet. Most of the planetary parameters used for this example are from Avatar: A Confidential Report on the Biological and Social History of Pandora. We already know that it is unlikely that a planet such as Polyphemus exist around Alpha Centauri A since we already have the capability to detect such large planets (sorry Jim). However, smaller Earth-size ones are still possible, such as Alpha Centauri B b.