Yes. Core allows you to sync your data with Xero. But before doing that, you must review and set the synchronization rules for a smooth and accurate data integration. Whether data between Xero and Core flows in one direction or the other (or both) depends on your sync settings. During data sync, Core either overwrites the duplicate data, if any, or leaves it as is, depending on your settings.
You can specify all your sync settings for Xero from the main menu > Productivity Tools > Integrations > Integrated Products > Xero > Xero Sync Detail > Sync Settings. Check Core Help Center for details on that.