You can definitely apply while still having your job, but you must be willing to work on it full-time for at least the duration of the Fellowship program. We hope you'll commit to it longer than that too -- if your startup is promising, you'll be working on it for many years to come.
However, I read an answer by one of the YC staff and they told the commenter that a current college student could apply, as long as they were willing to take the semester off. So it sounds like they are serious about the full time work requirement.
