The question of whether the average Roman could read is more complex than a simple yes or no. While widespread literacy like we know it today was certainly not the norm, literacy wasn't entirely absent either.
Estimates suggest that literacy rates varied greatly depending on social class, location (urban vs. rural), and time period. Elite Romans, particularly men, were almost certainly literate, often fluent in both Latin and Greek. However, among the lower classes, particularly slaves and rural populations, literacy was much lower.
Inscriptions found on buildings, monuments, and even everyday objects like pottery suggest a degree of functional literacy among some segments of the population. While not everyone could compose complex texts, the ability to recognize and understand simple signs and labels likely existed among a significant portion of urban dwellers. Think of it as being able to read street signs and shop names, but not necessarily Proust. So, while the 'average' Roman probably wasn't highly literate, pockets of literacy permeated Roman society, contributing to its vibrant culture and governance.
