Yes, it's possible, but you haven't provided any details as to how the data you want to keep can be differentiated from the data you want to replace. You mention multiple Sections, but not which header (every Section has three) and whether, for the headers you want to update, each Section's header is linked to the previous Section's header.

Here's some code to get you started:
Sub UpdateDocumentHeaders()
    Application.ScreenUpdating = False
    Dim strFolder As String, strFile As String
    Dim wdDoc As Document, Sctn As Section, HdFt As HeaderFooter
    strFolder = GetFolder
    If strFolder = "" Then Exit Sub
    strFile = Dir(strFolder & "\*.doc", vbNormal)
    While strFile <> ""
        Set wdDoc = Documents.Open(FileName:=strFolder & "\" & strFile, _
        AddToRecentFiles:=False, Visible:=False)
        With wdDoc
            For Each Sctn In .Sections
                'Assuming every header in every Section is to be processed
                For Each HdFt In Sctn.Headers
                    With HdFt
                        If .LinkToPrevious = False Then
                            'Process the header here
                        End If
                    End With
                Next
            Next
            .Close SaveChanges:=True
        End With
        strFile = Dir()
    Wend
    Application.ScreenUpdating = True
End Sub
 '
Function GetFolder() As String
    Dim oFolder As Object
    GetFolder = ""
    Set oFolder = CreateObject("Shell.Application").BrowseForFolder(0, "Choose a folder", 0)
    If (Not oFolder Is Nothing) Then GetFolder = oFolder.Items.Item.Path
    Set oFolder = Nothing
End Function
The macro includes its own folder browser, so all you need do is point it to the folder to be processed. As coded, it doesn't actually do anything, because you haven't hiven the required details.