Can Deployer migrate sites and have them appear in the Quick Launch?

Yes, While performing deployment, users can choose whether to show the sub-sites in the quick launch, or inherit the quick launch settings from the parent or not. 

Please note, in order to have these options, users must have chosen to read the navigation information from the source when loading the source content. 

Also, users must verify that the option "Migrate site quick launch" is enabled under Options > SharePoint > Commit Settings > Navigation Migration.