There is a relation between chronic stress in pregnancy (but like severe chronic stress, like homelessness, job loss, abuse, death of a partner, serious illness, etc.) and preterm birth and low birth weight, so in a way it makes sense that babies of mum's who experienced severe chronic stress in pregnancy would struggle in a lot of ways in the early months, due to things like failure to thrive, complicating health issues due to low birth weight and preterm birth, plus just the fact that chronic stress doesn't just go away (so it's definitely going to be more difficult and stressful dealing with being homeless, etc. after you give birth than before, which will have a knock on effect on baby). But that sort of chronic stress isn't really the same as just being hormonal or tired or a little sick, it's like serious stress.
But I wouldn't say that not sleeping through the night or being a high needs baby is so much a sign of stress. That's just called being a baby, and I'd say that's different from a baby who is truly distressed and unwell. I had a lovely, relaxing pregnancy with no stress, but I definitely had a high needs baby. She was perfectly happy, but she was happy in my arms and didn't STTN until she was just over 3 years. I think that's pretty normal (certainly is for all the mums I know with kids her age, who all also had lovely, easy pregnancies). She was never unhappy seeming or in pain though. But she wasn't a pram baby who just laid there and did nothing and was 'easy' if that makes sense. But if you are a stressed out person, you will definitely see that reflected in your baby though. I don't think it's so much a biochemical thing. Just if you are always wound up, they pick up on that and mirror your emotions. It's really obvious when we go through stressful periods (like I'm under a lot of work stress at the moment myself) and my daughter definitely picks up on that and it affects her too.