Sick?

I think I think the answer's yes.
No, these individual women (it's always women, isn't it?) aren't necessarily sick, but the society that produces this trend most definitely is.

The celebrity-driven fetishization of tiny little dogs is part of the same disease.
The Today Show did a segment on "reborns."
Anyone read The Children of Men? PD James was prescient.

Bogus baby boom

They’re called “reborns”: incredibly lifelike baby dolls that sell for up to $4,000 to adult women who collect them, change their clothes, and in some ways treat them like real babies.

“It fills a spot in your heart,” Lynn Katsaris told TODAY’s Matt Lauer Wednesday in New York as she cuddled “Benjamin” and “Michael” in her arms. A realtor from suburban Phoenix, Katsaris is also an artist who has created 1,052 reborn dolls and sold them to women around the world. She was one of three grown women visiting the show with five of the the bogus — but eerily realistic — babies cradled tenderly in their arms....
collectors, some of whom treat the dolls as real children, feel there’s nothing unusual about their passionate hobby.

Monica Walsh, a 41-year-old wife and mother of a 2-year-old daughter from Orange County, N.Y., has one doll – “Hayden.” And, yes, she told Lauer, she plays with her doll “the same way a man might make a big train station and play with his train station or play with his sports car, his boat or his motorcycle.”

Fran Sullivan, 62, lives in Florida and has never had children. She brought two reborns to New York, “Robin” and “Nicholas,” and said she has a collection of more than 600 dolls of all kinds, including a number of reborn dolls.

Sullivan told Lauer she rotates her dolls, choosing a new one to care for each day depending on how she feels. She talks to them as she would to an infant, but said it’s really not all that strange....

One woman in the BBC documentary, married and in her 40s, said she wanted a real baby, but was too busy to commit to caring for a real one. A reborn doll satisfies her maternal instincts, she said, without all the carrying on and mess.

Reborns, she said, “never grow out of their clothes, never soil them. It's just fabulous. The only difference, of course, is these guys don't move.”

Yup, that's the only difference... and when you do get tire of it, put him, er... it in the dumptster.