As other users have mentioned, it's going to be very,very unlikely that earth-level tech would be able to ramp-up in time to catch it - though the rocket is technically feasible, it's a bit of a stretch to assume that the scientists would be able to:
- Actually see the probe with their telescopes (the probe is very, very small - it took over 80 years to find Pluto!)
- Settle academic debate on what the probe is - remember, at a distance it will just be a speck of light indistinguishable from a perfectly mundane asteroid. The only chance for very early detection is that a very lucky radio signal (let's say the probe's been sent spinning, so the high-gain antenna is no longer pointed directly at earth, and its pings get picked up as a peculiarly regular signal by a radio observatory)
- Get funding for this tremendously expensive mission
- Build, test and launch the rocket
all within the launch window - including the time taken to match the speed of the probe, which will be a long time if you're using ion propulsion.
My suggestion: Treat it like Pluto
Intercepting a fast object is hard, but it's much, much cheaper to do a flyby - build a New Horizons-style probe, launch it with a number of very high resolution cameras and spectrometers and put it on a course to fly by and record as much information about the probe as possible.
E.g. to actually rendezvous with the probe:
but to simply fly by and take pictures, you only need to match the position:
With some luck (and some very fast cameras), scientists would plausibly be able to reconstruct the details of the golden plate (probably not enough to read the record grooves, however), but they would be able to determine the chemical composition and mechanical construction of the probe, determine that it was launched with chemical rockets by looking at chemical emission spectra and verify that it bears alien pictures and was not launched from their own planet (though the debate around that point might be an interesting subplot).
Without launching anything at all, they could get a pretty good estimate of where the probe came from (based on telescope trajectory measurements).
Voyager would also bear characteristic marks from deep space - miniscule holes from micrometeorites, possible a large missing chunk from a not-so-micro meteorite and (maybe) some residual charge from its trip through interstellar plasma.
(Note that these measurements can't be taken from the surface of Kerbin - no terrestrial telescope on the ground or in space has enough resolving power without being very close to Voyager.)