No.
If I’d not had the overwhelming desire to have children and be a mother, and struggled with infertility which made me more obsessed, then I absolutely think I could have had an equally happy and fulfilling life. More so even.
I had a wonderful full life before dd in many ways, loved my career, further study, amazing friends, close family, dog I adore, travel, books, music etc.
But that absolute craving to be a mum was always there. It’s a big part of why I ended up with my DH - he wanted the same thing and I knew what a good dad he would be. As we got closer to being too old with no success ttc/ fertility treatment I did try to start imagining my life without ever having children, and I think it could still have been happy but I definitely felt it would need to change quite significantly in order for me to be able to be happy.
Very very happily DD came along. I’m happy in a way I never thought possible even though it’s hard, I’m knackered, and physically and mentally I took a bit of a battering (postnatal anxiety for one thing).
Long winded way of saying - I think it’s perfectly possible to live a happy and truly fulfilled life without children but I don’t think I personally would have been anything like as happy.