The Park Hyatt in Buenos Aires? No, you cannot book in pesos. Very few hotels in Argentina allow that, as they would get crushed by inflation if people book many months in advance...

Upon check-out, your rate will converted to pesos at the official FX rate at the time. If you pay with a US credit card, you will receive a much better FX rate (close to the Blue rate). I imagine it would operate the same way if the hotel made you prepay for some or all of your stay.

(because of that system, there's no advantage to paying far in advance)