Most likely yes.

During the 1950s several studies were commissioned on the role of lower intelligence service members. One in particular was initiated by Dwight Eisenhower, while he briefly served as President of Columbia University. They concluded that these men still performed well in the military. Only the "clearly non-usable group of idiots and imbeciles," they concluded, should be exempted from military service and thereafter provided supplemental education. Remember that in the WWII era illiteracy and semi-illiteracy was still a problem in America, exposed during the WWII and Korean military mobilization and testing process. But as education improved and the demands lowered on the armed forces, the standards rose between the end of the Korean War (end of 1953) and the beginning of the Vietnam War (1965). In 1951 the minimum acceptable Armed Forces Qualifications Test (AFQT) score for the Marine Corps was 13. During the peak of the Korean War in 1952, it lowered to 10. But by 1960 the minimum score was 25 and went up to 31 by 1965. [Unfortunately I can't find the Army's minimum score, but it should be slightly lower than the Corps]

Those standards would have to change to meet the manpower needs for Vietnam. The Johnson administration, in keeping with its ideas about the 'Great Society' social reforms, initiated Project 100,000 which would set quotas on admitting lower scoring men into the armed forces. With modernization theory in vogue and a belief that institutions -- in particular the military -- could reform society from the top down, the Johnson administration cast this a means to lift thousands out of poverty and generally alleviate social ills. Of course, it also happened to meet the pressing need for more soldiers. Moreover, with rising AFQT test standards raised, about 1/3 of men called for the draft were being dismissed as unqualified for physical reasons or their AFQT score.

The AFQT divided testers into five categories, I through V, which correlated to a score on the AFQT. At one point the military correlated these results to IQ and found that class IV (which comprised the 10th to the 30th percentile of testers) was equivalent to roughly a 70-91 IQ. From what I've gather of the film and book, Forrest is supposed to have had an IQ between 70-75. At the time, this IQ would put him in the lower 15% of the population according to the US Army. For reference, 28% of WWII service men fell within this category IV group. Beginning in the late 1950s, category V testers, the bottom 10th percentile, were automatically rejected. Depending on needs, IV could be divided into different subcategories (A, B, C) and certain would be accepted for service.

Project 100,000 lowered the AFQT standards, though not below Korean War levels. The median score of those admitted was roughly 13 on the AFQT [recall the minimum Marine Corps score in the Korea War was '10'] and would put them at the bottom end of category IV. Most of them did not graduate high school (80%) and many had just a rudimentary reading knowledge (40% below a 6th grade level). Lisa Hsiao writes that 50% had an IQ below 85. Though the bottom 10% who took the test were still automatically disqualified, it could be overridden if the recruit/draftee passed an interview with an Army psychologist. [I have no idea what criteria that included.] With a low score such as this, you would be headed to the Army like Forrest. The Air Force and Navy had higher admission standards, as did the Marine Corps but to a lesser degree than the Air Force and Navy.

In sum, Forrest's 70-75 IQ would have likely placed him in the bottom end of category IV and eligible for service during the height of the Vietnam War. Even if he slipped into category V, he still could have enlisted if an Army psychologist believed he was fit to serve. During the other major mobilizations for WWII and Korea, he likewise would have qualified.

David Dawson, The Impact of Project 100,000 on the Marine Corps (Washington: US Marine Corps, 1995).

Lisa Hsiao, "Project 100,000: The Great Society's Answer to Military Manpower Needs in Vietnam," Vietnam Generation Vol. 1, 4 (1989).

At the My Lai war crimes trials, a clinical psychologist testified in the defense of Charles Hutto (who had confessed to killing civilians) that he did not adequately possess the capability to make the judgement on whether the order to kill civilians was legal, that his personality was marked by a total lack of creativity, a willingness to submit to orders from authority figures and a willingness to believe in others. I suspect a more modern psychologist might insert some qualifiers in there - unreasonable orders and believe uncritically.

This was enough to acquit him, essentially allowing him the defense that he was only following orders. His acquittal led to charges against 7 others being dismissed or dropped - implying that they were just as "psychologically subnormal".

Four Hours in My Lai, Bilton & Sim.