No. You will have to reconfigure Azure SQL Data Sync as SQL Data Sync creates a schema on each database participating on a sync operation. On that schema named DSS, it hosts tables to keep track on changes that need to be replicated to other databases.
Please remove SQL Data Sync on all databases participating on the sync before "refreshing" one of those databases. Otherwise, you may have to manually remove remnants on the databases that you won't refresh. And if you don't remove the remnants you won't be able to reconfigure SQL Data Sync after refreshing databases which may end you creating a ticket on Azure Support to get help on removing the remnants.