Sure, it's possible, but you are setting yourself up for trouble. Configuration, deployment, and troubleshooting will be constant hassles under IIS. If you really want to host internally, I'd setup an Ubuntu server in Hyper-V, use Nginx, and be done with it. On the other hand, if your shop isn't built to deal with managing a Linux server or hosting a Rails app internally, I think it would be more reasonable to consider Heroku or another PaaS before dealing with IIS.
EDIT: Coming from a background in Windows IT, I know that setting up a Linux server and managing it isn't always as easy as "do it and be done with it," so don't think I'm not sympathetic to where you're coming from. The thing is, while the "natural move" might seem like trying to do it in IIS, it is an unnatural move as far as Rails is concerned. My suggestion to anyone who isn't ready to make the plunge into both Linux and hosting their own Rails apps really is Heroku. Even with the know-how to configure Linux for Rails, I still use Heroku for all of my Ruby MRI apps.