Given that the content is the main ingredient of a site, I'd say it's very important.
Firstly, you're writing content for human visitors, not for search engines - or if you're not, you should be.
Secondly, plagiarism is theft. It's taking somebody else's hard work and claiming it's your own. It's unethical, to say the very least, and may get you into legal problems with the legitimate owner of your stolen content. Whether or not Google notices it and penalises the site for it (and they're getting much better at that) is really irrelevant. No reputable site owner will want to employ a copy writer who merely steals other folk's work. And before anybody tries to tell you otherwise, spinning is just another form of plagiarism, so don't bother thinking about that.
If you really want to make a career as a content writer, then I suggest you rethink your approach.