The validity of the Ballard score was tested on newborn babies down to 20 weeks gestational age, verified by early ultrasound examination. In these very immature infants, the correlation coefficient, tested against verified menstrual history, was 0.75 if performed prior to 24 hours postnatal age. After that it fell, largely because of rapid attrition in this vulnerable population. In short, yes it can be done, preferably sometime during the first day of life.
The neuromuscular portion is based upon passive and not active muscle tone. The score is actually designed for infants who are sick and even on ventilators, as long as they are not pharmacologically paralyzed.