Yes, I believe so. If I recall correctly, a pilot in training would have progressed through the T38 before being assigned to fly fighters or heavies.
My memory may be off though. I'm sure someone else can confirm or deny it for us.
They did until the AF switched the heavy drivers to the T-1 in 1997.
Taken from
http://www.baseops.net/militarypilot/The Path to Pilot Wings
All Air Force pilot candidates begin their flying training with introductory flight screening (IFS). Civilian flight instructors in Pueblo, Colorado administer the new flight screening program. Students fly the Mitsubishi Diamond DA-20 in their training. The program is a 40 day program that includes ground school and a 25 flight-hour flight screening course for up to 1700 students annually.
The next step in the process is joint specialized undergraduate pilot training, which prepares student pilots for the full spectrum of aircraft and flying missions. The term "Joint" denotes training with sister services such as the Navy, Marines, and Coast Guard.
Pilot candidates then attend either Euro-NATO Joint Jet Pilot Training (ENJJPT) or joint specialized undergraduate pilot training (JSUPT). ENJJPT is located at Sheppard AFB, Texas. The entire course lasts about 54 weeks. Students learn with, and are taught by, U.S. Air Force officers and officers from various air forces of our European allies. Student pilots first fly the T-37 mastering contact, instrument, low-level and formation flying. Next, they strap on the supersonic T-38 and continue building the skills necessary to become a fighter pilot.
Joint specialized undergraduate pilot training began at Reese Air Force Base, Texas, in July 1992 following the arrival of the T-1A Jayhawk. Undergraduate pilot training continued training all students in the T-37B Tweet and T-38A Talon until the T-1A arrived at each pilot training base. JSUPT was completely in place after the last UPT class graduated at Columbus AFB, Miss., in 1997.
The JSUPT program is accomplished through the cooperative efforts of the Air Force and the Navy. Joint training for Air Force and Navy students is conducted at Vance AFB, Okla., and Naval Air Station Whiting Field, Fla. Students complete primary flight training at these locations in the Air Force’s T-6 Texan II and Navy’s T-34 Turbomentor.
Other students complete the primary training at Columbus AFB, Miss., or Laughlin AFB, Texas, flying the T-6 Texan II. The USAF was first to phase in the T-6 as a replacement to the (now retired) T-37 Tweet. The first base to transition was Moody AFB, GA (no longer a UPT base) and the last base to transition was the ENJJPT program at Sheppard AFB, TX.
Following the primary phase of JSUPT, students move on to advanced training in one of several tracks. Students selected for fighter-bomber assignments fly the T-38A, concentrating on low-level tactics, instrument procedures, 2- and 4-ship formation flying and navigation training.
Prospective airlift and tanker pilots complete their advanced training in the T-1A at Columbus AFB, Miss., Laughlin AFB, Texas, and Vance AFB, Okla., where they are introduced to crew resource management techniques, air-to-air refueling, airdrop missions and radar positioning and navigation.
Students selected for the multi-engine turboprop track will eventually fly the C-130 Hercules and train at Naval Air Station Corpus Christi, Texas, in the T-44 or C-12 turboprop trainer. The training profiles closely resemble typical missions flown by the C-130.
Other students are selected to fly helicopters and complete their advanced training at Fort Rucker, Ala., in the UH-1 Huey. The helicopter syllabus includes operational skills such as low-level flying and combat tactics training.