As the title suggests, if I keep a mon infected with Pokerus in the PC, would it keep the ability to spread the virus indefinitely?
Yes. According to bulbapedia:
Whenever the game's internal clock strikes midnight, every Pokémon in the player's party has their Pokérus value decreased by one point. Once the Y value reaches 0, the Pokémon will be cured of Pokérus.
This means that if the Pokemon is not in their party, its Pokerus value would never be decreased and as such it would never be "cured" (though even when cured, it is still affected, it just loses the ability to spread it).