>An easy way to keep a "vessel" for future spreading is to always send the infected Pokémon to the PC, Day Care, Stadium 2 (in Generation II), Pokémon Box Ruby & Sapphire (in Generation III), or My Pokémon Ranch (in Generation IV) before midnight.
Source: Bulbapedia/ PokeRus
So, it will keep the virus. Since it does not spread when it is not in the PC, im gonna guess that it does not spread in the Day Care.
\m/o_o\m/