According to Java 7 documentation as well as third party vendors, it appears Java 7 should support AES-GCM suites:
AES-GCM is available in TLS v1.2. See [The Transport Layer Security (TLS) Protocol Version 1.2][1], section 6.2.3.3. TLSv1.1 did not add any cipher suites, and TLSv1.0 never had AES-GCM or the elliptic curve gear. (The elliptic curve stuff showed up in TLSv1.2 also).
The latest public build 80 of Java 7
does support TLSv1.2 after changing code to use SSLContext.getInstance("TLSv1.2") in case of socket programming or just declaring the -Dhttps.protocols=TLSv1.2 in case of HTTP programming.
does not support the AES-GCM cipher suite even under TLSv1.2, according to a request implemented only in a commercial build 191 of Java 7,
https://bugs.java.com/bugdatabase/view_bug.do?bug_id=8180834
Its interesting that the TLS_ECDHE_ECDSA_* cipher suites are showing up in your dump since they are TLSv1.2 ciphers.