If you're not looking to integrate the two themes into a single installation, then yes you can use both on the same site. Each would need their own instance of WordPress to work and you could install one theme in a different subdirectory:
e.g.
yourdomain.com <== Your Vantage installation
yourdomain.com/tickets <== Your Quality Control installation
You could share the user database by way of a
WordPress multisite installation. Thanks.