Interesting problem. Try these ideas to see if they might help.
First, getting the underlying SketchSegment after making the selection will help you get back to it - either to select it again, or find another spline in your sketch that isn't the original. Here's an example of getting the SketchSegment and re-selecting it.
Dim splineSeg As SketchSegment
Set splineSeg = Part.SelectionManager.GetSelectedObject(1)
splineSeg.Select False 'don't append it to the selection
Finally, after making a copy, you can traverse all of the SketchSegments in your active sketch, checking if they are splines, then checking to see if they are the same as the original spline (the Is comparison).
Part.Extension.MoveOrCopy True, 1, True, 0, 0, 0, 0, 0, 0
Dim sk As Sketch
Set sk = Part.SketchManager.ActiveSketch
Dim skSegs As Variant
skSegs = sk.GetSketchSegments
Dim i As Integer
For i = 0 To UBound(skSegs)
Dim skSeg As SketchSegment
Set skSeg = skSegs(i)
Dim c As Curve
Set c = skSeg.GetCurve
If c.IsBcurve Then
'found a spline
If skSeg Is splineSeg Then
'this is the original spline
'this is a different spline
Using swCurve.IsBcurve didn't work for me. Instead I used swSketchSeg.GetType = swSketchSPLINE.