Is it safe to assume that when a college’s tuition and fees are equal to the family’s EFC, they will not qualify for any financial aid?
Usually that is the case.
Yes it is safe to assume. And… depending on the school…if your EFC is below the total cost of attendance, you still may not get FA.
Note that a college may calculate an EFC that is different from the FAFSA one or what some other college calculates.