Does a Postgres VACUUM free up space for any database object?
After a VACUUM the table will be as big as before, just more of the space will be free and available for future INSERTs and UPDATEs. In other words, the file won't shrink (1). So the space will not be available for other tables, only for the table that has been vacuumed.

Note (1): Sometimes the file will shrink. If the last block is completely empty after the VACUUM, PostgreSQL will try to truncate all empty blocks off the end of the table.