Do note that your basic code won't work on tables with cells that are merged.
For code to return cell addresses in any table, try:
Code:
Sub Insert_R_C_into_every_cell()
Dim Rng As Range, aTable As Table, TblCell As Cell, cellvalue As String
For Each aTable In ActiveDocument.Tables
For Each TblCell In aTable.Range.Cells
With TblCell
cellvalue = "Cell_ID[" & .RowIndex & ", " & .ColumnIndex & "]"
Set Rng = .Range
With Rng
.End = .End - 1
.Collapse wdCollapseEnd
.Text = cellvalue
.Font.Hidden = True
End With
End With
Next TblCell
Next aTable
End Sub