no, its actually the opposite
All Pokémon with Pokérus that's not in a PC box gets cured every 12 midnight.
im not sure if they meant kl.12 every midnight or every 12th midnight, but the point is no pokerus isn't cured by depositing in a PC box
hope I helped :D
source
No, it doesnt. It will only get cured when you start using the Pokemon and then the time limit ends. Also if you cure that Pokemon at the Pokécenter with other Pokemon it will spread.
Source: Experience.