I can't say with any sort of definitive answer, I can only judge by what I have heard from veterans I know. Most of them have said that they heard nothing of the protests while they were in Vietnam. It was a world away, and never made it into the Armed Forces media. This is why they were so surprised, hurt and angry when they got home to accusations of baby killer and derision. So I would say most of the negative affects of the protests happened after they returned. On the other hand, many Vietnam Vets joined the anti-war movement when they got home.
My father is a Vietnam Veteran, and he was not only affected by students' protests while in Vietnam but also when he came home. Students who were protesting the war were also some of the ones who yelled nasty comments at my dad when he returned to the States and who neglected to realize that every time a soldier such as my dad went off to the war, that meant that one of them did not have to go.
When my dad was in Vietnam, it was bad enough that he and other soldiers witnessed the government and military officials' constant wavering, but it also didn't help their attitude when they felt that nobody supported them--they felt left out to dry by their leaders and normal citizens such as the students.
Interestingly enough when American soldiers returned to the States for good from Vietnam, the same people who seemed so concerned about bringing them home did nothing to help them make the transition back into the real world.
The protests by students (and others) against the war in Vietnam is said to have had a very negative impact on American soldiers in that war.
The major impact was on the morale of the soldiers. "Morale" means their enthusiasm, willingness to fight, and general attitude about the war. Military experts say that an army's morale is critical to its ability to fight.
The protests can be said to have reduced morale because they reduced the soldiers' feeling that what they were doing was good and that it (and they) had the support of the people for whom they were supposed to be fighting.
This decrease in morale is said to have led to things like increased drug use among soldiers and reduced willingness to fight.