No from a labor law perspective.
From an Argentine tax perspective, if the remote worker was an Argentine citizen then the answers to the questions above might change considering that Argentine citizens are deemed Argentine tax residents (unless they meet criteria to lose their tax residency).
Because of that, Argentine tax resident individuals shall pay Income Tax in Argentina on their Argentine and foreign sourced income (e.g., income arising from a local or foreign labor relationship).
However, this circumstance should not affect the individual’s foreign employer since the individual would be liable to assess and pay for their own taxes in Argentina. Please bear in mind that if the employer was an Argentine entity then they shall withhold and remit income tax arising from the local labor relationship to the Argentine Tax Authority.
If the foreign national employee engages in activity interacting with the local market then it might be construed by the Argentine Tax Authority that such engagement constitutes a permanent establishment under ITL’s provisions, and that such income is effectively connected to the foreign entity by the foreign national employee’s activities in Argentina. In this case the foreign entity should assess Income Tax in Argentina for its Argentine-sourced income.