Can Localities returns city names on a postcode input?

Absolutely. There is a field named postal_town in the predictions on postcodes returned by Localities which indicates the most populated city or post office city associated to a postcode.

Postcode suggestions are available in the countries listed in Postal code coverage. In the United Kingdom and the Republic of Ireland, postcodes also carry has_addresses, so you can go one step further and list the individual addresses behind a postcode.