Yes, MVC sites can be hosted with us.
In order to avoid versioning issues and allow users to use whatever version of MVC they wish, we do not preinstall it on the servers. Instead, simply upload your choice of System.Web.Mvc.dll (or Microsoft.Web.Mvc.dll as needed) to the "bin" directory of your website. No further action is required in order to run an MVC site.
MVC also has a facility to allow for routing, for SEO friendly URLs. This requires the use of a wildcard script mapping for ASP.Net. If you understand the effects of this, and wish to enable it on your account, this can be done from "Website Settings" in Helm.
Many MVC sites based on more recent versions require full trust in order to function, as well as using integrated pipeline. These settings are not set by default, but can be set for free at any time from the "Website Settings" page for the domain in your control panel.