Run Asp.Net Mvc as OWIN middleware?

No, MVC depends on System.Web.dll (and thus IIS).

Currently ASP.NET MVC doesn't run on OWIN. Web API will because it's been decoupled from System.Web, specifically HttpContext. This is the main dependency that prevents MVC from running on OWIN as well.

Some alternatives that do run on OWIN are FubuMVC, Nancy and Simple.Web