If you only consider object placement when defining the area group constraints, routing might not be able to form all required connections. The following image shows a variety of area group constraints that all allow routing to form connections. In all three of these cases the routing never has to leave the defined area groups to complete its routing.
In contrast there are two common errors that affect routing and area group constraints. The left side of the following image shows a missing area group for an object. In the second case, all objects are within separate area groups but the two groups are not adjacent. In this case the router has no way to complete the routing of its nets without violating an area group constraint. The router fails to find a legal solution.