Yes.. Also, stated in gocoastguard.com (see copied criteria below). But I think in your case since you are "prior service" may NOT fall into this category. So I would still refer to your recruiter statement.. sounds like you should be fine especially if you have a ship date already set
Applicants must meet the following criteria and successfully pass several screening tests:
Be a U.S. citizen or a resident alien.
Be between the ages of 17-27 (up to age 32 if attending an A school) for active duty. (If you are 17, you'll need parental consent.)
Reservists must be between 17-39.
Prior-service personnel should contact their local recruiter for specific criteria.
Have a high school diploma. GEDs are accepted in very rare circumstances.
Have no more than two dependents (spouse, children, or someone dependent upon you for support).
Pass the Armed Services Vocational Aptitude Battery (ASVAB) test.
Be medically cleared by the local Military Entrance Processing Station.
Undergo a credit check, security clearance check, and a criminal record review. (2nd and 3rd degree misdemeanors and or felony convictions are disqualifying.)