Student Visa to Tourist Visa?

Im going to be staying in Brazil from February to June. I Received my visa from the Consulate for 6 months, the day before the first day of class to the last day of class. However, I will arrive to Brazil before the first day of class and  leave a month after the program ends. My question now is, would i be able to stay in Brazil before and after the dates of my Student Visa (Vitem IV) my country of citizenship is exempted from a tourist visa (Visa Free) Can I just stay in the country the remaining of the time as a tourist?

Great question. I would imagine since working backwards (Tourist VISA to Student VISA) you have to leave and re-enter the country, so perhaps the same applies. I am not sure about this topic though and I would like to find out too.

Leaving the country would require going to at least Argentina, then it might be cheaper to just pay the $R8 per day for overstay

Not quite that easy since if you look at the Tourist Visa, it does not permit remunerated work or any studies while in Brazil. You would be much better off to start the course and (with proof of the course duration) go to the Policia Federal - Departamento de Estrangeiros before the expiry of your visa and request an extension (prorrogação de estada). I have no doubt that if you haven't completed the course they would extend the visa to permit completion.