Not quite. He joined ROTC, was commisioned a 2nd LT. in '72, at a time when the Army was not taking all that many ROTC grads onto extended active duty. He did serve 3 months active duty September to December of '75. Here's what Wikipedia has about it:
While a sophomore at Princeton, Alito received the (low) lottery number of 32, in a Selective Service drawing on December 1, 1969. In 1970, he became a member of the school's Army ROTC program, attending a six-week basic summer camp that year at Fort Knox, Kentucky, in lieu of having been in ROTC during his first two years in college. Graduating in 1972, Alito left a sign of his lofty aspirations in his yearbook, which said that he hoped to "eventually warm a seat on the Supreme Court."[4]
He was commissioned as a Second Lieutenant in the Signal Corps after his graduation and assigned to the Army Reserve, one of nine in his class to receive a commission in the Army Reserve. Following his graduation from Yale Law School in 1975, he served on active duty from September to December, 1975, while attending the Officer Basic Course for Signal Corps officers at Fort Gordon, Georgia. The remainder of his time in the Army was served in the inactive Reserves. He had the rank of Captain when he received an Honorable Discharge in 1980.[5][6]
It sounds as if he either requested delayed entry, or even more likely was just not offered an active duty slot. One guy I work with was RIFed from the Army Signal Corps about that same time, so likely they weren't taking many ROTC grads. I know that in '73 the Air Force was offering all non-scholarship grads a Reserve slot, although I think those were active reserve, not inactive. Another guy I once worked with was also an ROTC grad who was not sent to active duty, and about that same time. I think he was Chemical Corps, and he also was released as a Captain, in spite of never serving any active duty or active reserve time. It was pretty common in that period which marked the beginning of the end of the Vietnam War, and particularly the US Army's involvement in it, save a few advisers to ARVN units.