Edits made -- Okay, after raising a few eyebrows, squinting, and re-reading your question several times, I think I know where the confusion is. My original answer still applies to your original question. I am talking about the keyword tags displayed on StackExchange sites along the sides and content of pages, not HTML tags that affect SEO and structure a page in the "view source". These two meanings of "tag" combine at the end of my answer because search engines use HTML tags to know what the keyword tags are... I have attempted to be more clear here...
Yes (to your second question). Keyword tags link related content together and, if implemented into the design correctly, can give search engine context-specific clues about the content on each page and their relationship and value to one another.
Homepage content is, I believe, weighted more in general (at least the area in the first 800x600 px is). The homepage Stack Exchange sites do so well because of their proper use of
<h1>...<h6> HTML tags, placement and flow of content, and contextual linking of related, relevant results. And because the content changes frequently, search engines like Google can know it's a reliably up-to-date website.
Take away the keyword tags and the site would still be indexed, but would lose great relational value to both users and search engines. In the end, (at least on Stack Exchange), it looks like the keyword tags are just
<a> HTML elements, but being so close to the main article/content as they are provides a substantial value, compared to links off the side of the page or at the bottom, disconnected to the relevant content.