I've installed a fresh Orchard 1.5.1 as an Azure "web-site" (technology preview). No modules have yet been added. I activated multi-tenancy, created one tenant, and then logged into the tenant site.
The base site is:
http://anthemdentistry.azurewebsites.net
The tenant site is:
http://anthemdentistry.azurewebsites.net/dentist
I browsed the Gallery, and attempted to install a theme. I was immediately relocated to the parent/base site and told "access denied."