I am not super familiar with Zen, but my understanding is "yes, sort of". Zen come from Mahayana path and I believe it retains those teachings and cosmology, but it's not as central. Looking at it on Wikipedia, it looks like Zen is all about teaching enlightenment with very little importance placed on much else, so in that regard, yes.
I don't know much about Daoism and Buddhism, but I know a guy who compliments people in the West who claim to be Daoists on their excellent Chinese. Most of them don't get the joke (it seems many important texts have never been translated).
Concerning Buddhism, don't certain sub-branches of Zen buddhism come quite close to the Western "no magic" version?