I do not know if anyone has already answered that, so I will allow myself to do that. Sorry my limited language skills, I am French.
Already, this sentence is interesting: "It seems to be possible to detect rotation in an object without reference to anything external."
Indeed, it is possible in General Relativity. The rotation of an object deforming the geometry of the space-time alters the curvature of said object. This is called the Lense-Thirring Effect. Measuring this variation of curvature makes it possible to determine whether the object is rotating and to determine the speed of this rotation.
In addition, I do not know what you mean concretely by "absolute non-rotation", but if I understood your question, you are asking if an object may not be rotating. If that's the case, yes, it's possible in theory.
