If you insert such an object in the document, then Cut it (and, presumably, the paragraph break following it) from there to place it in the clipboard, you could use Find/Replace, where:
Find = empty, but Heading 1 Style specified
Replace = ^&^c
A macro to do the same thing:
Code:
Sub Demo()
Application.ScreenUpdating = False
With ActiveDocument.Range
With .Find
.ClearFormatting
.Replacement.ClearFormatting
.Text = ""
.Replacement.Text = "^&^c"
.Format = True
.Forward = True
.Style = wdStyleHeading1
.Wrap = wdFindContinue
.Execute Replace:=wdReplaceAll
End With
End With
Application.ScreenUpdating = True
End Sub