A more interesting event will be when crewed spacecraft "pass" the Voyagers. Betting this won't happen is basically betting that humanity will destroy itself.
Basically, sometime in the future, Earth is dying, so everyone has to leave to some faraway planet within 100 years.
The first intrepid explorers leave at T-100 years, expecting to be the first to arrive. A few years later a new craft leaves that can travel faster and will get there sooner. This goes on and on until it comes down to a betting game of how late can you wait until leaving, while still being the first to arrive (and thus claim ownership/leadership, etc.), with people coming up with all kinds of hair-brained schemes on the best time to actual leave.
IIRC, it kind of turned a little into Hitchhikers Guide kind of ridiculous near the end.
Probably not what you're thinking of... It sounds like something Asimov would have written but nothing comes to mind.
Would like to read.
(Oh, and they show that colonizing the universe would be surprisingly easy. This has obvious implications re: the Fermi paradox.)
[1] http://www.sciencedirect.com/science/article/pii/S0094576513...