Yes. Supported Cloud Document fields appear as inputs in the Pre-Upload modal, and each selected file maintains its own values and generated path.
P.S. Discover Azure Integration, the easy way to upload files from any Salesforce record to Azure. Find it on AppExchange: https://appexchange.salesforce.com/appxListingDetail?listingId=c9e71bd6-5bab-4182-a461-b82d4f971183