Question: Does inline CSS and JavaScript really affect site SEO?

Answer: 
Hardly. What counts for a search engine is textual content, it will filter out everything else.

I assume CSS comes into play with search engines when they determine whether a portion of text is visible on the page, or hidden for the purposes of SEO. But even there, whether the CSS inline or in a style sheet won't make a difference.

One could argue that the more CSS and JS a page contains, the less weight do search terms have on that page. But I think that argument is invalid, because any non-content content will simply be ignored altogether.
I don't think most spiders actually execute Javascript before parsing the page. If there's something you really want indexed, it's best to put it on the page as simple content. Bring it in via Ajax, constructing it on the fly via javascript, et. al, certainly will only hinder its SEO value. Tricky links that take form after being constructed by Javascript are also bad form -- a simple site map probably yields better value.