Poking around the DreamHost support wiki and terms of service, I can't see anything stopping you. You can run an Arc interpreter in the background, so long as it doesn't eat too many resources, and I can't see anything stopping you from forwarding requests to it.
However, it will not be officially supported in the same way that Ruby and Python are, so you'll be on your own when it comes to fixing problems. It might be better to use their private hosting service so that they don't complain about your Arc process (which they may do if a bug causes it to behave badly). Although this means it runs on a private virtual server, you still get all the same support and software as with the shared service.
