No, With the Admin Permission Set, the users can see the About Mass File Download Tab but can’t modify the settings. Only System Administrator can Modify the App configuration setting on the About Mass File Download Tab.
PS: View Mass File Download, Salesforce file download app on Salesforce AppExchange: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000EcsAOUAZ