No, the Docker container comes with only the software, I’d suggest you to use the humann:3.0.0.a.4.plus.utility.dbs image which also includes the mapping utilities.
You can specify the path in which the HUMAnN databases will be installed with the last humann_databases parameter, but what I would do is to have both the UniRef and CHOCOPhlAn databases in a local directory and mount it via volume binding and run HUMAnN with the --nucleotide-database and --protein-database parameters in order to point to the correct database location