Being well nourished does seem to help if you give blood. It is especially important to have enough iron in your diet.
I have only once given blood, many years ago. I had been on a diet for a long time and I hadn't eaten at all that day. Someone asked me whether I had eaten. I said "no" and she said "you're going to faint." It sounded so absurd that I just smiled at her. I wasn't afraid or nervous.
When it was my turn, the nurse stuck a needle in my finger to get a sample to check my blood type. She poked it around against the bone for what I am sure was longer than necessary.
I woke up on the floor while they were giving me smelling salts. They said that I was the only person who they had seen faint BEFORE they had inserted the needle to actually draw blood. They asked me whether I was epileptic and refused to let me give blood.
While walking back to the office, the woman I went there with was disgusted and said that if I fainted, she would just leave me on the tarmac. I went out for a good meal and then I went back and insisted that they let me give blood. They were reluctant but agreed. There were no problems the second time.
More recently during a diet, I spent a morning without anything more nutritious than water. I felt that I might faint. I felt too weak to move but as I live alone, I decided that I had better not lose consciousness. I had a couple of glasses of orange juice and that perked me up.