This is just a variation of Graham's working solution. It does address the extra paragraph that results when inserting a file:

Sub ScratchMacro()
'A basic Word macro coded by Greg Maxey
Dim oCC As ContentControl
Dim oRng As Range
Dim lngFile As Long
Dim varFiles
  'Set a range where you want the first control
  Set oRng = Selection.Range
  'Ensure that the range does not include a selection of text
  oRng.Collapse 0
  varFiles = Split("Block1|Block2|Block3", "|")
  For lngFile = 0 To UBound(varFiles)
    'Add a content control to the range
    Set oCC = ActiveDocument.ContentControls.Add(wdContentControlRichText, oRng)
    oCC.Title = varFiles(lngFile)
    oCC.Range.InsertFile "E:\Templates\Template Building Blocks\" & varFiles(lngFile) & ".docx"
    Set oRng = oCC.Range
    oRng.Characters.Last.Delete
    'Move the end of the range out of the control
    oRng.End = oRng.End + 2
    oRng.Collapse 0
  Next lngFile
lbl_Exit:
  Exit Sub
End Sub