Can a GFI shutdown a second non-GFI outlet?
Yes -- GFCIs are provided with a set of LOAD terminals so that other receptacles, light fixtures, or hard-wired devices can be connected in a way that provides them GFCI protection as well.  It is common to see this used so that one GFCI protects several receptacles -- there are even "dead front" GFCI devices that have no receptacles themselves, but are solely intended to protect "downstream" loads.