Sure it can. If it changes the underlying structure of your content. For the most part it should have little effect, but some templates require you to make significant enough changes to matter. For example if you are using a template that is custom coded to display multiple posts on your homepage then you switch to a template that shows only a single page or vice versa. Any change to your site can change your ranking. Having said that... I changed a site from Joomla to WordPress... obvious structural changes and it made no difference to my primary keyword phrase ranking. This is mainly because the content was similar, and that Google relies so heavily on factors that are offsite.
I think it's not so good to change the theme of your blog too frequently. According to the experience of my colleague, if you change the themes many times in a period of time, it is difficult for search engine to catch your new articles submited in that period of time. Therefore, you'd better choose a theme and keep it stable.
What does the graphics have to do with the content and permalink structure ? Can someone please explain EXACTLY how changing from one WP theme to another will affect your SEO I a negative way ? If all your settings are the same, and everything is still in the same place and can still be found on the same link, how does changing the stupid graphics, and colors impact SEO ? I think you are all paranoid.
I think you got your answer mate.. Feel free to PM me if you have got any doubts related to SEO of wordpress blogs..