Is it possible in Illustrator to display all of the anchor points is not selected objects?

No. Moreover, during displacement of the node visible only the nodes on the curve being modified. A simple example: draw a donut, then there is a circle with a hole. Make sure that the object is a single object, i.e. a compound path (for reliability, ctrl+8). The floating node of one circle is external or internal: to display only nodes of the selected circumference, and not the other, although both part of the same composite curve.

For this is the white arrow direct selection (A). Select a point and move, the other point will not be seen, but the quick guides in the mouse will tell me where the other reference point.