Usually if its anything thats short term they won't move dependents until they have more permanent orders. It's dependent on the length of the school. They wont pay to move dependents only to move again a few months later. If it's a longer A school... possibly. Each A school is very different in many ways.
If the seat time for the A school is 20+ weeks, then usually yes. Less than that, no. C schools are counted separately. There are only a few schools long enough, AECF, SECF, Nuke, language school in Monterrey, some of the CT ratings at Pensacola, maybe AT, and I think GM school at Great Lakes. Maybe a few others. I'm sure I am forgetting a couple. Hold times do not count toward the 20 weeks. The orders must specify that dependents are authorized.