Typically, anchor text does carry through 301 redirects but it is difficult to use this as the sole means of link building in any site. Though this sort of link building does typically work, it may not work for all the resources that are available and present. Google reserves the right to score and rank this type of link building and this means that it could be potentially denied. This process helps to determine the trust for links and redirects which helps to keep those using the site safe. All of the redirects that are present in a site are logged similarly to all the links that are present, which makes using 301 redirects as your sole form of link building a tricky and perhaps dangerous method of link building.
Since this is a typically abnormal way to build links, it may be difficult to build a site solely from these redirects. Webmasters and designers should be worried more about creating a viable and useful resource that will garner good, solid links rather than focusing on potential ranking boosts through the use of anchor texts and redirects. Links that are given freely and flow organically are the ones that last the longest and do the most good for a site in the long term. Because these organic links are easier to follow and help sites more, it is beneficial for a site to strive to become a good resource that is worth adding this type of link to.