Normally, no:

“Ask the Good Master if the Unsullied have their own officers.“
“You must set your own officers over them. We train them to obey, not to think. If it is wits she wants, let her buy scribes.”

But Dany’s Unsullied do:

“When she had commanded the Unsullied to choose officers from amongst themselves, Grey Worm had been their overwhelming choice for the highest rank. Dany had put Ser Jorah over him to train him for command, and the exile knight said that so far the young eunuch was hard but fair, quick to learn, tireless, and utterly unrelenting in his attention to detail.”