|How the Kepler Mission detects planets around other stars. Image Credit: NASA|
The short answer is yes. We don't expect to learn any groundbreaking new facts about Venus, the Sun, or the Solar System. But we can use the fact that we already know so much about these objects to make use of this transit by testing our techniques to study planets around other stars.
One of the main techniques astronomers use to study planets around other stars is called the transit method. A tiny fraction of planets around other stars have their orbits oriented just right so that they pass between their parent star and our view from Earth. We can't see the dark spot of the planet crossing the star from dozens of light years away, but we can measure a tiny drop in the amount of light from a star. NASA's Kepler Mission uses this technique in its search for Earth-sized planets around other stars.
When planets are discovered by the transit method, we have to infer a lot of the planet's properties. There are sources of error, including what we know about the parent star, how active the parent star may be, what the parent star looks like in detail, and so on. From our vantage point on Earth, the Venus transit will have similar properties to a Neptune-size planet transiting a sun-like star (since we are close to Venus, it appears larger in proportion to the more distant Sun than it really is). So, we can test all sorts of sources of error and uncertainty.
The Hubble Space Telescope will use the transit to test how we probe atmospheres of extrasolar planets. Venus has a thick and cloudy atmosphere, and we know what that atmosphere is made out of. Some of the light from the sun will pass through Venus's atmosphere and pick up some information about the atmosphere's composition and structure. Astronomers have used this same technique to probe the atmosphere of planets around other stars. Since we already know what Venus's atmosphere is like, we can use the Hubble observations to try and recover that answer, and see how good (or bad) our current studies are.
Astronomers, like Captain Cook 243 years ago, have set sail to study the transit of Venus from around the world (and even outside it). The science may have changed, but the opportunities afforded by this rare event are still launching expeditions centuries later. When the next transit happens in 2117, will there still be scientific value in the transit? Perhaps, though it is hard to imagine what. Yet during the transits of 1874 and 1882, could the astronomers of that time have imagined us measuring transits of other worlds around other stars? Of measuring atmospheres with orbiting telescopes and electronic equipment? I doubt it. So perhaps we should close with a quote from William Harkness, director of the U.S. Naval Observatory in 1882. Change the word "twenty-first" to "twenty-second", and these words still ring true:
"There will be no other transits of Venus till the twenty-first century of our era has dawned upon the earth. When the last transit occurred the intellectual world was awakening from the slumber of ages, and that wondrous scientific activity, which has led to our present advanced knowledge, was just beginning. What will be the state of science when the next transit season arrives God only knows. Not even our children's children will live to take part in the astronomy of that day." (gathered from space.com)