Without actually seeing your code, and relying only on your description, I think you are unlikely to be able to run this site successfully on any low-cost shared host. but I have no way of knowing for sure without seeing the server load created.
SH does not have “hard” CPU limits, but will curtail access to your site if it is negatively impacting others sharing your server and their ability to operate their sites.
500 concurrent connections, even without MySQL, might be too much. I could be wrong, and you should probably ask DreamHost directly yourself (http://dreamhost.com/contact.cgi).
I’m not trying to discourage you, but you should know up front what you are likely to encounter.