My understanding is "Yes, but always at the Handicapper's discretion".
There are, I understand, a number of circumstances in which this discretion might be exercised so as to not move a person up a grade:
1. Despite having secured the required 7 points, the rider is judged to lack the skills to race in the higher grade. This has been applied to a number of young "hot shots" in the past, who are fit and strong but dumb as a meat axe. It is primarily a safety issue, and the rider is (as they might see it) "held back" to allow them to gain a bit more race sense before being thrown in the deeper end in the new higher grade. those moving from B grade to A grade, for example, with limited race experience might find the willingness of some A graders to lean on each other, and chop wheels , and do other stupid stuff, a bit confronting.
2. The person may be judged to be someone who will struggle and therefore be dangerous in the higher grade because they win the lower grade through wheelsuck-and-sprint, and so might not have the required fitness to race well or safely in the higher grade. There are plenty of riders who have done this, and they either cause an accident or are dropped back down after a few weeks because they can not hold a wheel.