No. Residence/work permit agreements are based on nationality, not on resident status. .
"Agreements" between nations (by definition) may be based on nationality, but, at least in Argentina, I don't see how residency and work permits are tied to nationality. While it may be "easier" for a foreigner who is a citizen of another Mercorsur country to get residency and a DNI in Argentina, If they qualify for residency, I don't think it matters what country a foreigner is a citizen of in order to obtain Argentine residency and the DNI.
Temporary residency in Argentina may be based on having a work contract with an Argentine company that is registered with Argentine migraciones to hire foreigners, but it can also be based on being a student or having a passive foreign income (just to name two) and I believe it is possible for
any foreigner who is a citizen of
any country to work in Argentina if they have at least temporary residency and the DNI.
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.
I have no doubt this is correct and it is also the case in Argentina. Temporary and permanent residency in Argentina do not grant the right to work in any other Mercorsur country. This is the answer to Fiscal's question.
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.
As this applies to citizens of Argentina getting residency in Brazil (without actually living there?), I assume that would entitle them to work in Brazil, but it raises a separate question: As a citizen of a non-Merorsur country, can a foreigner (like Fiscal) apply for and receive a residence permit in Brazil that would entitle them to live and work in Brazil without waiting two years (in other words, without becoming a citizen)?