I would like to allow a user to click an ultraGrid at runtime and be able to see the selection handles (white dots) and re-size the control like we can in the visual designer. Is this possible?
No, this is functionality provided by the VS designer, a control just defines its selection rules and the designer handles the rest. Typically to support resizing the control you set the Dock or Anchor properties, which make the control resize itself along with changes to the size of the form.