Pokerus doubles EV's gained from defeating any other pokemon, to be precise, its a free Macho Brace. Also, even if it gets cured, which the games portray as the Pokemon becoming immune to it, it still doubles the EV gains after that, any mon that has been infected has it forever. However, it can only spread to other Pokemon in your party (specifically, the ones next to it in the party list), if it is in its active state. So it definetly IS useful to infect some random mon you dont really intend to use, and store that in the PC so you can use it to infect more mons in the future. It doesnt have any downsides, and at least in the official games, it has (roughly) a 1 in 21845 chance to appear on any wild pokemon, so its rarer than shinies, but it can infect your party without you catching the pokemon.
These chances are probably massively increased for Reborn, similar to its much higher shiny rate.