If you already have received gifts, send a thank you note now, send them as you go along, same with brides who get gifts before the wedding.
Woah, there I was thinking that wedding gifts were for a couple, not just a bride. I wonder if grooms/fathers are also have the weight of thank you cards on their conscience.
The very last thing I'd expect a friend with a baby to bother herself with was a thank you card for the gift I got for the baby. She might have post natal depression. She just might not feel up to it, might just be exhausted. She might be anxious about spending a seemingly small £30 on cards and stamps for all the gifts when her maternity pay is a pittance and she's worried about paying over a grand a month in childcare soon. She might be busy looking after other kids as well as the baby. She might spend all her time adoring the baby and watching Neighbours. I really don't care, it's a time for her and her baby to take priority.
If I received a card I'd love it, especially with a picture, because I enjoy seeing a friend's pride and joy. But I absolutely would not expect one, nor would I think less of someone for not sending me one.
I love sending cards, I still send Christmas cards and that's a dying tradition. I like to think would send cards if I received baby gifts, because I like getting creative and using my fountain pen, but I have no idea what my baby would be like, how I'd feel after birth, etc.
If anyone got me a gift and then got pissy about not getting a card, I'd only wish they'd let me know so I could reimburse them for their troubles and not bother with their pomposity in future.