No. Currently, subdomains may reference only a main directory (e.g., www.your-site-here.net) or a subdirectory one level down (e.g., www.your-site-here.net/subdirectory1/).
You cannot assign a subdomain to a subdirectory within a subdirectory (e.g., www.your-site-here.net/subdirectory1/subdirectory2/).
Note: You can point a subdomain only to a Turbify-hosted website. Although you can't create a subdomain that sends your visitors to a site hosted elsewhere, you can set up A and or CNAME records for that purpose via your Domain Control Panel.