Short answer is yes they did, although it wasn't the Mexican peso per say, but the spanish dollar or the spanish pieces of eight. Long answer, back during the 17th and 18th century the colonies found themselves having a shortage of legal british currency since most was given the motherland due to the existence of a massive trade imbalance at the time. Stemming from this issue, people back in the day used to accept spanish silver and gold as a valid form of currency. Coins who's origin was the silver mines of central Mexico; so in a sense yes, the USA did accept and use the peso, but not in the literal sense. In fact, the lack of currency was such a big issue back during colonial times that people in massachusetts used to accept iroquois shells as a valid means of exchange. So the idea that the us used to utilize what at the time was the hegemonic super power is not out of the fields of reality.