I don't know what your skill levels are, so I could only guess at the right answer to that question.
According to this from the opengarden site the current installer requires root access, which you do not have access to at Dreamhost.
You'd have to install mono yourself, make sure you were on an Apache 2 server (some DH sites are still on Apache 1.3), install mono yourself, gather the resources to resolve a few other dependencies (install some other stuff), and then find away to install the whole beast so that it would work without relying on the installer. I'm not saying it can't be done, but I don't think I could do it. YMMV