My question is this: should I build this from scratch, or should I use Ruby on Rails or Drupal? I haven't built an app in either, so I'm not sure if one would work well in this situation. Any advice? Thanks.
The sub-domains stuff is actually pretty hard in every CMS I've ever used, so I suspect it's a challenge in Drupal, too. Besides that, I don't know that a community-style CMS like Drupal brings you any benefits, does it? By this, I mean, are users connecting in some way? It seems like you're just looking for a way to make scaling out to multiple machines a nightmare. RoR, also, is a CRUD building tool. It's really good for building CRUD apps. I'm not sure what you're building is a CRUD app...but, then, I don't know what you're building.
If you're thinking straight up, "build a website" in the Weebly, Synthasite vein, then you probably don't want a framework or CMS at all, except perhaps for the management layer (which doesn't have to scale much at all). Perhaps relevant: I helped a free website hosting operation scale up several years ago, and he achieved his 1.5 million websites scale from a handful of off-the-shelf machines (in 2001, or so) by deploying to static pages. He also could add new machines and re-hash without any trouble at all--no database was involved, except for the creation and management of pages. I believe Weebly does the same (and they're kicking ass with nearly a million websites now, and scaling up without even having to think hard about it, because they designed it appropriately for scaling).
I think maybe you need to spend a bit more time thinking through your problem domain before deciding what the solution looks like.
To many people today, a blog and a traditional website are almost the same thing, so perhaps a multi-user multi-blog framework might get the job done.