No, Flash does not auto-update on a Mac. Never has.
Flash Player plug-in
CVE-ID: CVE-2009-3794, CVE-2009-3796, CVE-2009-3797, CVE-2009-3798, CVE-2009-3799, CVE-2009-3800, CVE-2009-3951
Available for: Mac OS X v10.5.8, Mac OS X Server v10.5.8, Mac OS X v10.6.2, Mac OS X Server v10.6.2
Impact: Multiple vulnerabilities in Adobe Flash Player plug-in
Description: Multiple issues exist in the Adobe Flash Player plug-in, the most serious of which may lead to arbitrary code execution when viewing a maliciously crafted web site. The issues are addressed by updating the Flash Player plug-in to version 10.0.42.