Yes. This only works for whole paragraphs, if highlighted. It does include any whole paragraphs within table cells. It does not include sentences that are highlighted with paragraphs that are not highlighted. This parses through all the paragraphs, checking to see if the current paragraph is highlighted (with whatever color), and if it is, copies it to another document. It then prints out the document with all the highlighted paragraphs.
Sub PrintHighlights()
Dim r As Range
Dim i As Long
Dim count
Dim PrintJob As String
Dim myDoc As Document, PrintDoc As Document
Application.ScreenUpdating = False
Set myDoc = Application.ActiveDocument
Application.Documents.Add
Set PrintDoc = Application.ActiveDocument
myDoc.Activate
i = ActiveDocument.Paragraphs.count
Selection.HomeKey unit:=wdStory
For count = 1 To i
Selection.MoveDown unit:=wdParagraph, count:=1
' see if paragraph is higlighted yellow
' if using different color then change this to whatever it is
If ActiveDocument.Bookmarks("\para"

.Range.HighlightColorIndex = wdYellow Then
' set range for current paragraph
Set r = ActiveDocument.Range( _
Start:=ActiveDocument.Bookmarks("\para"

.Start, _
End:=ActiveDocument.Bookmarks("\para"

.End)
' select range if range is not empty
' copy to printing doc, then move back
If r.Text <> "" Then
PrintJob = r.Text
PrintDoc.Activate
Selection.TypeText Text:=PrintJob
Selection.TypeParagraph
myDoc.Activate
Else
End If
Else
End If
Next
PrintDoc.Activate
ActiveDocument.PrintOut
myDoc.Activate
PrintDoc.Close (wdDoNotSaveChanges)
End Sub