No.

Unity catalog enforces permissions on the table level (and catalog and schema etc), but not on the storage level.

Unity itself uses a managed identity or service principal for storage access btw. This id should have access to the data lake.

What you can do is create dynamic views to make a row-level security setup.

https://learn.microsoft.com/en-us/azure/databricks/data-governance/table-acls/object-privileges#row-...