False. In that sentence, the word is clearly referring to the noun usage, as in a profession.

Being a wet nurse was never a profession.

From Oxford Dictionary:
nurse (noun)
a person trained to care for the sick or infirm, especially in a hospital.
Similar:
caregiver
attendant
carer
Florence Nightingale
nursey
candy-striper
(verb)
1. give medical and other attention to (a sick person).
"she nursed the girl through a dangerous illness"
Similar:
care for
take care of
look after
tend
attend to
minister to
2. feed (a baby) at the breast.
"the women nursed their babies"

She didn't say that there were zero female nurses prior to Florence Nightingale. There were. But Nightingale created the educational pathway that opened the door for women to become nurses through special women's colleges. Remember, women weren't allowed in most colleges back then.