The bottom line answer to your question is “Yes”. The photos of massive numbers of helicopters moving troops into battle, providing supply lift, and taking wounded to medical care are truly reflective of the massive use of helicopters by the US in Vietnam. As early as 1963, the Army began to evaluate new doctrine and tactics for the use of helicopters in warfare, and in 1964 the 11th Division (test) was established in the US to test air mobile doctrine and capabilities. By 1964-5, it was determined to try the concept in combat, and the 1st Cavalry Division (airmobile) was formed and sent to Vietnam. As it deployed, it contained over 700 aircraft (mostly helicopters). Soon, around its base at An Khe, massive air-carried assaults on enemy forces became routine. Further development of the concept in later years of the conflict resulted in the formation of the Army's 1st Aviation Brigade in 1966, which supported units throughout Vietnam, and the use of massive air assaults with many dozens of helicopters at a time became nearly routine, throughout the combat zone. The 1st had 43 Companies, 8 battalions, and over 850 aircraft.

In total, over 11,000 helicopters (including 7013 UH-1 variants) were used by the US in Vietnam, of which more than 5000 were lost in combat.

Some references I would recommend for further reading:

Allen, Matthew. Military Helicopter Doctrines of the Major Powers, 1945-1992. Boyne, Walter J. How the Helicopter Changed Modern Warfare. Chinnery, Philip D. Vietnam: The Helicopter War