More than 800 employees at St. Elizabeth's Medical Center in Brighton will join the Service Employees International Union. Nearly three-quarters of those voting approved a plan to join Local 1199 of SEIU United Healthcare Workers East, union leaders said. St. Elizabeth's, the flagship of the Caritas Christi Health Care chain, is the first large Boston hospital to be organized by the SEIU, which in 2007 began a drive to unionize Boston's major hospitals.