The Alexandria School Board voted last night not to give the names, addresses or telephone numbers of city students to armed forces recruiting officials despite an assertion that without the cooperation of the nation's public schools, reinstitution of the draft could be hastened.

"Are we sending out junk mail?" asked Lt. Col. Lee Scarbrough in response to questions about the military's request for student lists made last month to Washington metropolitan and Baltimore County school districts. "No, not unless literature funded by taxpayers describing opportunities for training, jobs, advanced education and service to one's country is junk."

The action, school board members were quick to explain, did not constitute a vote of "no confidence" in efforts by the armed forces to recruit Alexandria students, but rather reinforced a general school policy of not releasing directory information about students. In fact, many board members added, military officials are allowed to recruit weekly at T. C. Williams High School, the city's only high school.

A law passed by the last session of the Virginia legislature allows school systems to provide student addresses and telephone numbers to military officials. In Northern Virginia, Falls Church, Prince William County and Manassas have agreed to provide student lists. Arlington County has declined to do so, and Fairfax County has yet to make a decision.