Yes! The carry will depend on how old the baby is and how big mommy's chest is.
Nursing in the wrap must not be considered an achievement, it's just convenient when you have no choice or when baby is already in the wrap. Of course if you're at home you won't put your baby in the wrap just for nursing.
Once you and your baby are used to nursing in various positions, you can nurse in emergency situations in everyday life: while picking up a toddler from preschool, in the bus, walking in the street, shopping...

During your baby's first days, to accelerate the production of mature milk, get a lot of skin-to-skin contact with him.
If you spread every tail and pass it'll be as if you were dressed (nice if you're having family over or are at the hospital in a double room) and your body will naturally do what it needs to.

- Nursing in the Cradle Carry:
This is quite nice with a newborn once you've had a chance to get acquainted with the carry, don't try everything at the same time!
A quick tip: when baby's really hungry he can start nursing once he's in the first strap, and you can finish adjusting the carry as he nurses.

Baby can also nurse in a Cradle position in the cross passes that are in front of you when you have him in Back PWCC (see pic).
- Nursing Tummy-to-tummy in PWCC :
This is a great position if you have an overactive let-down since baby's head is slightly higher than your breast.
This can be done with a newborn once breastfeeding has become easy for you.
You never know until you try the position, so don't hesitate and try several times.
This is the position to use for babies who don't like Cradle Carry.
It's also interesting for a mother with large breasts

Put your hands in the wrap under baby's bottom, shift him to the side and slide him down to the appropriate level so he can latch. The wraps stretches, take advantage of it!
Baby's head must not be covered by the wrap, but you can pull the strap all the way from your shoulder to get some slack and hide his head without pinning it to your breast.

- Nursing outside PWCC without taking off the wrap:

Important points:
For more privacy, you can cover Baby's head with the wrap, but it's important to hold his head with your hand as he latches: the fabric will just hide his head, as Baby should be able to freely move away from the breast.
Don't use the cradle carry if your Baby suffers from acid reflux. It's better to nurse him in a vertical position.

Vidéos :
Nursing in the superior strap of the cradle carry :