It really depends on the nature of your site, if you are serving up lots of dynamic content pulled from a database, then obviously MySQL performance is going to have a significant impact on overall site speed. However, if your site consists of mainly static content, with the occasional dynamic page, then it is going to have a lesser impact. Of-course, this is a bit of a simplification, as there are ways to speed up the dynamic content through intelligent caching etc.
My own sites tend to be affected more by server load than MySQL performance. I have noticed that whenever my sites are slow (thankfully not a regular occurrence), logging-in via SSH invariably shows a high server load.
If MySQL performance is of paramount concern to you, perhaps you should be looking at a real dedicated server with root access etc, rather than the dedicated/shared hybrid offered by DreamHost. DreamHost does have a partnership with hosting.com, perhaps one of their dedicated offerings would suit?