No. Residence/work permit agreements are based on nationality, not on resident status.
Same happens in the EU; if you are not a EU citizen but you're a legal resident in a EU country (even if you have permanent residence) you are only allowed to work in that country, and NOT in any of the other 27. You will be able to travel freely as a tourist to any Schengen-area country, though.
For some Mercosur countries, for example Brazil, even if you become a naturalized Argentine citizen you have to wait 2 years to be able to obtain a Brazilian residence permit. In other words, natural-born Argentines are able to obtain Brazilian residence immediately, but naturalized Argentines have a 2-year wait from their naturalization date before they can apply.