Yes, in shut down mode, it is possible to send SNMP trap, when a security violation occurs in a switch port.But for this, the port security should be enabled in shutdown mode, not in violation mode.
According to the port security config of cat6500 switch,
If a security violation occurs, the Link LED for that port turns orange, and a link-down trap is sent to the Simple Network Management Protocol (SNMP) manager. An SNMP trap is not sent if you configure the port for restrictive violation mode. A trap is sent only if you configure the port to shut down during a security violation.
For detailed info, refer this link.
http://www.cisco.com/en/US/products/hw/switches/ps700/products_configuration_guide_chapter09186a008007fa13.html