If this would happen on a truly large scale, like covering 60-80% of the population, then it would probably cause a small temporary downside movement, because it would be a negative event - someone sending people empty wallets, hoping that they would use them and steal their coins/
Not to mention the glaring privacy implications. If the person/company/government/etc who sent the paper wallets kept track of which wallets were tied to which physical postal address, they could easily tie real world identities to Bitcoin users and monitor which people were using it.