transit - Is it easier to learn more about the seasonal changes in an exoplanet's atmosphere when the exoplanet orbits a binary star system?

From a recent ScienceDaily article, we have this...

Scientists detected the new planet in the Kepler-16 system, a pair of orbiting stars that eclipse each other from our vantage point on Earth. When the smaller star partially blocks the larger star, a primary eclipse occurs, and a secondary eclipse occurs when the smaller star is occulted, or completely blocked, by the larger star. Astronomers further observed that the brightness of the system dipped even when the stars were not eclipsing one another, hinting at a third body. The additional dimming in brightness events, called the tertiary and quaternary eclipses, reappeared at irregular intervals of time, indicating the stars were in different positions in their orbit each time the third body passed. This showed the third body was circling, not just one, but both stars, in a wide circumbinary orbit.

The gravitational tug on the stars, measured by changes in their eclipse times, was a good indicator of the mass of the third body. Only a very slight gravitational pull was detected, one that only could be caused by a small mass. The findings are described in a new study published Sept. 16 in the journal Science. "Most of what we know about the sizes of stars comes from such eclipsing binary systems, and most of what we know about the size of planets comes from transits," said Doyle, who also is the lead author and a Kepler participating scientist. "Kepler-16 combines the best of both worlds, with stellar eclipses and planetary transits in one system."

Which brings up some interesting questions. Namely - could we learn more about the exoplanet when it can undergo multiple transits in front of each star?

With single stellar systems, we often can only see the exoplanet's transit when the exoplanet is in a single consistent position (analogous to seeing the Earth only during Northern Hemisphere winter, and not at any other time).

But with multiple stellar systems, we might be able to see the transit during Northern Hemisphere winter and during another season too (we might even be able to see transits for even more seasons)