There is no easy way to accomplish this, any solution will require a considerable amount of work on your part.
The info-window is just an HTML Div Element, therefore you can use Dojo's dnd/moveable module to move this div around. As for the anchor remaining in place, this will require you to come up with some code that listens to the Dojo events, then recalculates the positioning of the div which forms the anchor. This will probably not be trivial, and I can't offer any tips for this as I've never attempted such a thing.
An issue I can think of is that the div that contains the anchor and the info-window will start covering the map as it will get larger as you move it further from the anchor point. This will prevent you from interacting with the map. You may want to look into using pointer-events CSS properties, but these are only supported in IE9+.
