PokéBase - Pokémon Q&A
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They can get through if their levels,stats and caught location is correct.If they are not,they won't be able to get through.

Source: Neoseeker

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PID may need to be correct too, this impacts pokemon caught with the "wild encounters always shiny" AR code on.

Source: Pokecheck, personal experience.
So say I started with Snivy and then caught the other starters while battling Cheren and Bianca. Will Tepig and Oshawatt make it through the Poke-Bank filter?
Probably not as you cannot catch the other two starters in Unova.