The State and Country Picklist feature in Salesforce allows users to select states and countries from predefined, standardized lists, instead of entering them manually into text fields2. These picklists are based on ISO-3166 standard values, which are internationally recognized codes for identifying countries and their subdivisions. Therefore, before migrating the data, the consultant should confirm that all state and country values in the source data are ISO-3166 values, otherwise they will not match the picklist values in the target environment.
Contact Multi-Addresses Enabled is a setting in EDA that allows users to store multiple addresses for a contact, such as home, work, or mailing address. This setting does not affect the migration of state and country values, as long as they are ISO-3166 values. Every contact having a state and country value is not a requirement for the migration either, as these fields are not mandatory in EDA.
Reference:
1: Configure State and Country Picklists - Salesforce3
2: ISO 3166 - Wikipedia
3: Enable Contact Multi-Addresses - Salesforce