Yes, the pokemon will be able to spread it around, even after you deposited it. Pokèrus has a value of only staying on a Pokèmon, for about 24 hours. 24 hours until it fades and a little smiley appears on it's summary, or whatever you would call it. After that, a pokèmon cannot obtain it, nor spread it.
People usually infect their current pokèmon party, then deposit at least one with the virus, to spread it around in the future.
Hope that answers your question!