No. If the probe were a few light hours closer (i.e. at Pluto’s for example) the star than Earth is, it would see the exactly same transits, but a little earlier. It would have to be very far away in order to see transit times changing due to geometry.

Does the transit method only work for planets close to the star? What is the most distant known transiting planet?

In theory, it does not matter how distant the planet is. However, in reality the probability of a transit drops when the planet’s orbital distance increases. In addition, more than one transit is needed to make sure that there is a potential transiting planet there (finally, radial velocity measurements are needed to confirm the object has a planetary mass). For this reason all transiting planets are hot Jupiters (with the notable exception of Gliese 436 b, which is a hot Neptune orbiting a red dwarf).

The most distant known transiting planet is HD 17156 b, which orbits its star in highly elliptical orbit every 21 days. Its transits were found with the help of amateurs. The planet itself was discovered earlier. The COROT team may have spotted more distant planets, but if they have, they haven’t told it us yet.

I ask mainly out of curiosity, I can’t imagine what new information such a fact might provide, but it would be a nice confirmation of . . . I don’t know. But it would be really cool!

Remember the DVD analogy above? Seen edge-on, the odds are good that other planets in the system will transit their star

Playing Devil’s advocate here, at present this is uncertain due to the lack of orbital inclination measurements for most extrasolar planets. (Plus the fact that currently all known transiting planets are the only known planets in their solar systems). So far there is only one pair of planets in an extrasolar system for which mutual inclination is known (two of the terrestrial-mass planets orbiting a pulsar).

While it seems likely that planets do form in a disc, who knows what their subsequent evolution would do to the initial system… if planet-planet scattering is responsible for the eccentric configurations of some systems, there could potentially exist systems of planets which have high mutual inclinations and depart strongly from Ye Olde Sol Systeme Modele of planets orbiting nicely in the same plane.