As we know democracy is about

Participation of all the citizens in decision making.

By being literate, the people in a democracy have the following advantages:

One does not have to depend on hearsay to understand information.

One can be better informed and take better decisions in democratic election process.

One can read and understand any legal documents without depending on others and avoid scope of being cheated.

Yes, being literate doesn't mean one will be rational in their thinking, but being literate will take care personal informed decision by the person, be it rational or irrational.

It is just not for democracy, it applies universally. To understand any system properly, one needs to be properly educated.

Hence education and literacy play a very important role in democracy.