if it transmits and shuts off its transmitter, would the signal still be traveling towards earth?
I don't have a precise answer for your title question, however to give you some feel for how much energy (in terms of effective radiated power) is transmitted from space probes. Here is a good reference discussing http://pdf.aiaa.org/preview/1968/PV1968_1103.pdf [Broken], using the Mariner satellite (1969 flyby to Mars) as an example.
I would assume your question is hypothetical since "both Voyagers flew beyond the orbit of Pluto/Neptune in 1989. Neither flew by Pluto, which was elsewhere in its orbit at the time. It was never planned that the Voyagers would visit Pluto."
If one of the Voyager sats were in the neighborhood of Pluto, then if it transmits and shuts off its transmitter, would the signal still be traveling towards earth? It would be reasonable to assume, this is the type of transmission made, since leaving the transmitter on after sending the data would be wasteful of power budgeted on a probe.
Once radio waves are generated, they will propagate across space (for the same reason that light will radiate across the universe even when its stellar origin has long since been extinguished). It does not matter that the transmitter is turned off afterwards, the energy radiates through space. I don't know what type of antenna they had on board the Voyager probes.Its efficiency would be improved if it was transmitted, using a directional antenna pointed at earth (This ties in with the concept of effective radiated power). But even an omnidirectional antenna will radiate some signal towards earth.
Depending on the gain of earth-based antennas, some very faint radio signals can be discerned, not only from the edge of our solar system, but from deep space. A fun way you can assist in listening for intelligent radio signals from deep space is with the SETI project. You can analyze data collected from the Arecibo Radio Observatory on your home PC. (I've been participating since 2000).
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