When a link domain is enabled, it is also used to serve your Hosted Pages, which will also become accessible via HTTPS after following these instructions. But, as Matt Cutts says in this video, the page rank and anchor text will flow through the shortened link and that there shouldn’t be any harm in using them…as long as the URL shortener is using a 301 redirect. See if you are using Classic Analytics (ga.js) or Universal Analytics (analytics.js).