So when you say that your private server can't handle the load, do you just mean that your PS hits its limit of memory or CPU? If that's the case, then you're fine because your processes are just killed or just slow down. Since this just affects your server and not anyone else, DreamHost doesn't need to take any drastic action other than maybe recommending that you buy increased limits.
If you've bumped up your PS to 100% and are still having problems, then you've maxed the capacity of a dedicated server. Since the server is now, by definition, dedicated solely to you, you're not affecting other customers and aren't going to be subject to any drastic actions.
BTW, this is all assuming that you have both PS for your web server and PS for you MySQL server.
I don't recall ever reading about any DreamHost reaction to DDOS against a customer site here on the forums, so I can't provide any real advice here.
Have you contacted DreamHost for pre-sales support questions via the following form?
If you're talking about buying multiple maxed out PS'es or dedicated servers, I'm sure they'd be happy to answer your questions. They seem to be happy enough in answering questions from us lowly $9.95 a month shared hosting customers. (my self-categorization, not theirs)
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