I note the underlined.
Yes, to date, the Governor has not authorized arrest powers. They are to work with the Border Patrol, not independent teams.
http://governor.state.tx.us/news/press-release/20025/
“Texas put out the call and you have answered. Your mission is clear - to be a visible presence to deter criminal activity - and contribute additional eyes and ears to assist law enforcement and Border Patrol agents along the border,” Gov. Perry said. “At stake are the lives of innocent people along both sides of the border, and the safety and well-being of communities across the state, and our nation, placed in jeopardy by the criminal activities of transnational gangs and drug cartels.”