Yes, using the import application feature user can import their existing data but please ensure that the question XML and question types should be similar in both source and target application. Below is the help guide.
https://communityforce.zendesk.com/hc/en-us/articles/360057801251-Manage-Site-Settings-General-Settings-Enable-Import-Responses-from-Existing-Applications
Can a user import answers from the existing application without copying each and every data
