My first experience with this thing isn't great. Only because I haven't had one. My kid's been active probably 30-40 Sim days, so it looks like I'm not getting one. So, they don't all get them, especially those made in Create a Sim.
I have yet to have a CAS toddler get one. Even a few of my born in game babies don't get one, or if they do, they never get the option for them to become real imaginary friends (the living doll step), even if they do nothing but play with the doll all day. Also, they've never gotten one, no matter how many times I've moved them in or out of houses. The ones that didn't originally get one, still didn't get one even after moving.
Right now, my youngest sim had to be given one by a friend as a child, and has to build the relationship up from scratch to get to the living doll stage, in order to turn it real- he already knows most of the potions and has the imaginary friend one in his inventory- in roughly 10 days before he becomes a teen.
By contrast, his older twin sisters both got a doll as babies, in the mail, and as soon as they became children, the dolls became living dolls and are now both real sims, gaining them a 'brother' and a 'sister', respectively- thanks to their little brother's chemistry skills. The Twin that had the IF become a boy is now romanticly involved with him.
I've had other families where the older children all got dolls, then it'd skip a couple kids (one family had 11 children, as I was trying to see how many kids they could have before she got too old), and then the younger ones got dolls again.
So it rather seems to be hit or miss as to whether they all get one or not as well as when or how.