The need to have adequate food, water and shelter drives human beings to go above and beyond. When the amount of money that is available is diminishing, yet the costs remain the same, people can quickly become desperate to maintain the life they lead. This is true regardless of nationality. These individuals seeking to meet their survival needs will turn their eye on the locations in which they feel their efforts will be the most fruitful.
Yes, illegal immigration will probably get worse as a result of the Mexican Peso reaching historic lows. Since the value of the peso is weakening, citizens of Mexico are more likely to leave their country and live illegally in the United States to seek labor that pays a better wage.
Poverty is a big problem in Mexico, which is one reason why immigrants from Mexico move to the US, so it is likely that there will be some increase in the number of people trying to move here illegally. Drug cartels and the corrupt goverments are anothe reasons why people move here.
As the peso continues to lose value more and more impoverished Mexicans will be driven to seek work in the United States. Given that the United States is such a critical trading partner Mexico, the loss of purchasing power relative to the dollar will inevitably further disadvantage Mexicans leading them to seek work that pays in the stronger dollar.