dd1 was 2.2 yrs when dd2 was born at home, and watched the birth although was sleeping for most of my labour, if that makes sense. We had planned ahead, and made sure she had her own nominated adult who she knew well for the whole of labour, delivery and for a few hours afterwards. We agreed that if she got even the tiniest bit bored or upset she would go to this persons house, to have a "special play time". We didn't need to do this, she was absolutely fine, and even helped DH to cut the cord. She was not in the least traumatised or frightened. She remembers it now, pretty much exactly as it happened, and loved to tell people about how she had helped her sister to be born.
I guess it depends on the child and the mother. dd1, even then, was a very cool customer, who wasn't phased by much. I withdraw into myself when in pain, so the shouty thing didn't apply. We just told her I was having to work very hard to get the baby out of my bump through my special bits so we could snuggle and hug it.
I'd say that going with your gut insinct is nearly always right; you know yourself and your little one best.