I am confident that the pages in your persistent navigation are given more weight by Google.
On each of my sites I have a sidebar that presents a categorized list of links to the important pages that I want everyone to see. They could be there because I want them to be given attention by google, because I want them to have an opportunity to be seen by every visitor, because they are new and I want to promote them, or because they are important sales pages. The strategies and categories are different for every site.
If someone lands on your site and sees three links to other pages, what message does that send? Nuthin' here? If someone lands on your site and sees a great presentation of inviting topics, what message does that send. If you want people to see what you have, don't make them dig for it. If you have great content, get it out there and flaunt it.
Some of my good friends are designers who proselytize the concept of minimalist design. They think that I should have no more than three to five links on any page. They "tisk tisk" when they look at a site like mine. But, each of my sites has more traffic than all of theirs combined.