There are far too many variables involved in the questions that you asked to provide a reliable answer, given the information you provided. In order to even guess, we would need to know:
Is the site static or dynamic?
If Dynamic, how efficiently is it coded?
HTML, PHP, perl?
MySQL, and how efficiently is it coded?
With or without fastcgi?
Are apache re-write rules being used?
(and so on, these are just a few of the questions…)
“The point” is how any site will perform in such a circumstance depends on the answer to many of the above questions (as well as others), and what you consider to be a “hugh amount” of hits.
There have been Dreamhosted sites that survive slashdot, and digg, reasonably well, and there have been others that go “paws up”. This is a classic “YMMV” question.
Bottom line - these are shared servers and, as such, share resources between a large number of users. If you are planning for that level of traffic, on a consistent basis, you should seriously consider whether a dedicated server would be more appropriate.
That is not to say you might not be fine, and Dreamhost has stated they they will try to work with you to “weather” such temporary bursts of load (by a short-term move to a different server, etc. as appropriate for the circumstances), but you need to realize the inherent limitations and capabilities of shared servers. If your site brings a shared server to it’s knees, you can expect for everyone on that server to be negatively impacted (which, or course, includes you!)