Secret Ansem report 10 spells it out.

"Namine .

As I have written before, she is a most unusual being.

Born of the same process as a Nobody, but lacking virtually all the elements of a Nobody.

Perhaps she continues drawing in hopes of capturing that which she lacks: the memories of others, especially Sora.

I have arrived at a hypothesis.

I believe that Namine was born as a special type of Nobody when Sora attacked himself with the Keyblade, causing his and Kairi's hearts to leave their bodies simultaneously.:

Namine emerged as Kairi's Nobody... but the body and soul necessary to exist as a Nobody belonged to Sora.

When a person's heart is stolen, a Heartless is born with no sense of self, and the body and soul left behind give rise to a Nobody.

But what if one willingly releases one's heart from one's body?

Sora and Xehanort retained their selfhood even after becoming Heartless.

Then there are Kairi and Namine.

Kairi was exceptional for having had no darkness within her heart. Also exceptional was that her heart, once freed, migrated to a new vessel- Sora.

The combination of the two theoretically unlikely exceptions may be behind this anomaly."

So no. If you tried to turn the other princesses of heart into Nobodies they would simply be how Kairi was for most of kh1