Yes. For a college junior, the drafting team loses the right to sign them although I'm not sure if this technically happens on the "signing deadline" or when they return to school. They would be draft eligible again after their senior year.
For a college senior, I suppose if they don't sign and don't return to school they would be a free agent, although if they don't sign it's probably because they'd rather not play baseball.
For a high school kid that doesn't sign and chooses to attend school the choices are basically:
- Go to a four year school and be eligible again after your junior year
- Go to a Junior College and be draft eligible the next year (draft eligible every year out of JuCo)
- Do the Carter Stewart and go to Japan!
I'm not sure what the options would be for the delinquent high school draftee who chooses not to sign, refuses to attend school, and does not want to sign in an international league. I'm guessing they would try to sign an independent league contract for a year and then might be a form of free agent???