Some interesting feedback from Google recently suggested that changing the design of your website can impact search engine rankings, even if the content stays the same. I think that this largely refers to the location of items on a page, where some positions are considered more significant than others. Designers may consider it inconsequential to move items, but the search engines may not think along the same lines.
My experience is that the majority of web designers have little knowledge of SEO, and you should assume that the relationship between web page layout and search engine performance will not have come into their thinking at all. To be fair, it’s usability that should be the most important aspect of the design, but there’s a reasonable compromise to be made between this and other considerations such as graphic design and SEO. Most experienced website managers will have seen examples of redesigns causing both positive and negative impacts on search engine rankings; it is a bit of a lottery, but with careful thought, SEO problems can be minimised.