Let’s get this out of the way quickly.
Using any VCS requires you to do merges. The more frequently you commit, the less merge pain you have. With a distributed VCS like git or mercurial, you also have to fetch from a remote repository, merge and push. Merging does not disappear, so deal with it.
Why am I stating the obvious? Because I have seen a couple of cases now where people have switched from centralised VCS (cvs, svn style) to distributed and believed that it will help them reduce problems in code. The thing that helps you reduce problems is tests. Running your tests under a CI server just creates a tighter, automated feedback loop. Of course, you have to update/fetch, merge, commit/push for your CI to be useful.
Hmmm, did you see what flashed by? Your CI server does not give you a tighter feedback loop; it is frequent commits that gives you a really tight feedback loop. The CI server will sit idle for as long as you don’t commit and push.