No. The Coast Guard is a full branch of the armed forces. See 10 U.S. Code § 101(a)(4). They're unique among the other four for having a law enforcement mission during peacetime. The CG used to report administratively to DoT until the Bush years when Congress moved them with other entities to create DHS.
When I served overseas in the Navy, Coasties were intermingled with us. Their mission is much broader than what you imagine.