No that's not how green threads work, which was the whole point. You can have an API that presents you with "threads", but not have any actual threads underlying it. It is just a state machine running async, event driven code under the hood. The overhead of such a system is no higher than it is using the naive and error prone event loop approach.
Here's a paper on using userland threads to get the API advantages of threading, with the scaling advantages of event driven programming: http://static.usenix.org/events/hotos03/tech/vonbehren.html