Thanks for all your feedback. I contacted support directly just a few minutes ago and Mike S responded (very quickly) that it may cause a problem, but that I should make use of their 97 day moneyback guarantee, and sent me some additional pointers, including an offer to check the process's resource usage after I run it. Great idea!
To address specific questions:
You are correct. I am not putting these files up to be archived, which I see is specifically disallowed. They are being served, and not just served to a single company, but to a large group of disparate people. They are accessible to anyone with an internet connection.
I don't imagine this would be a problem because I'll be well within the limits. Your other comment about using "find" on the local files could potentially be very useful if rsync is killed for being too resource intensive.
That's a good idea. I've emailed Mike S asking about that. edit: He suggested I could be nice by using "nice". Another good idea!
Lots of websites pull from multiple sources these days. I'm not sure that having the html come from a different place than the media makes the place with the html the "website" and the place with the media a "file server". Html files are also files which are served. Seems like an even split to me. I was also thinking of hosting the css file on DreamHost, too, which makes the distinction even more blurry. For a technical service to say "I'm not going to define what a website is, but I know one when I see one" is, in the long run, untenable. Not that it should matter, but these files are not what some people in the hosting world might think of as "files" as opposed to website media. They are .jpg images. So, it's not like I want to use DreamHost to host my company's Microsoft Office documents, which I think might be the concern.
The files in question are legit, and are being served to the public, not being used as an archive.
We already have a dedicated server which we get for free (because this is a volunteer gig for a local charity). Unfortunately the server is on a really slow connection, so although it can calculate and serve small amounts of html relatively quickly, it doesn't have the bandwidth to serve thumbnails or full size photos without the internet connection getting bogged down.