If you run full SSL site then yes, you should use HTTPS for every link, anywhere and everywhere. This means all content, all menus, all XML, all RSS, all assets, all redirects, etc. And yes this does affect SEO because it's 1 less 301 redirect when they are put directly into SSL mode.
Google does not like to be redirected around too much. There are (un)official statements through the years that assimilate Gbot getting annoyed around 5 redirects. 0 redirects is better than 1 redirect, therefore better for SEO.
Another thought on SSL, imagine you have a platform that automagically updates urls when you change them on an item. There is an old link laying around somewhere that goes to a page/item that you have changed the url of like 4 times. When Gbot visits the old link, it's chained into https, followed by 4 redirs chained through the automagic 301 maker. You just hit 5 redirs. If your automagic url crafter had used https, you would still be "below the limit".