Eggs can get infected, but not as soon as you get them, only through contamination from fellow pokemon in the party. I really can't remember if I caught it in Gen VI, because I simply brought it over from Gen IV. One Saturday night, my Luxray in Platinum battled a wild pokemon for training. It was late and I was tired, getting a small shock to the system when reading the PC nurse's description of Pokerus. It was off to the races from there. I caught it there with no traded pokemon, and by the time I noticed the same nurse message in Omega Ruby, I think I had one with Pokerus in the party. I think, I can't remember, Synchronizing Natu migrated from Gen III, don't think they got exposed.
I don't think it's changed since Gen IV, the chances are very low, and can come out of nowhere.