I've wondered similar things about more recent periods of immigration, like how common it was for Gentiles living in and near Jewish neighborhoods to be able to carry on a conversation in Yiddish like James Cagney, but I know a lot less about social conditions during the colonial period, so I thought I'd take my chances on that question instead.
(Mods, I was hoping my question would be considered as conforming to the 17th century theme. Did I need to tag it myself? How does that work?)