Atahualpa's conversion to Christianity would have been a major propaganda victory for the Spanish. It would have made it much more difficult for them to justify their invasion of the Inca Empire on religious grounds. As a result, the Spanish might have been forced to negotiate a peace treaty with Atahualpa, or even withdraw from Peru altogether.
2. Atahualpa might have been able to maintain his independence from the Spanish.
If Atahualpa had converted to Christianity, he might have been able to use his new religious status to rally the Inca people against the Spanish. He could have argued that the Spanish were not true Christians, and that they were only interested in exploiting the Inca people. As a result, he might have been able to unite the Inca Empire and defeat the Spanish.
3. Christianity might have spread throughout the Inca Empire.
If Atahualpa had converted to Christianity, he would have likely promoted the new religion among his subjects. As a result, Christianity might have spread throughout the Inca Empire, and the Inca people might have become a predominantly Christian nation.
4. The history of South America might have been very different.
If Atahualpa had converted to Christianity, the Spanish conquest of the Inca Empire might have been delayed or even averted. As a result, the history of South America might have been very different. The Inca Empire might have survived, and it might have become a major power in the region. Alternatively, the Spanish might have been able to establish a more permanent and stable colony in Peru, and South America might have become a predominantly Catholic region.