The results of each dbcc checkstorage operation are recorded in the dbccdb log. Updates to the text and scan workspaces are not recorded there.
The dbccdb log must be sized to handle updates to the tables. The log requirement is related to the number of tables and indexes in the target database. It is not related to the target database size.
To minimize the log requirement and the recovery time, use the truncate log on checkpoint option with dbccdb.