The short answer is 'no'.
You have no control over your clients' e-mail applications. You have no control over the incoming e-mail formats - with plain text having no compatibility with fields. If you add material to messages, you damage their evidential value in the event of a future legal action.
In theory you can add to an e-mail message, either incoming or outgoing using a macro (or in the case of incoming a script attached to a rule), but I would avoid fields. At its simplest it would be as follows, but you could replace the reference input box with a lookup to the Access table.
Open a new (or existing) message and run the Test macro.
Code:
Sub Test()
Dim olMsg As MailItem
On Error Resume Next
Select Case Outlook.Application.ActiveWindow.Class
Case olInspector
Set olMsg = ActiveInspector.currentItem
Case olExplorer
Set olMsg = Application.ActiveExplorer.Selection.Item(1)
End Select
AddData olMsg
Set olMsg = Nothing
End Sub
Sub AddData(olItem As MailItem)
'Graham Mayor - https://www.gmayor.com - Last updated - 07 Jul 2021
Dim olInsp As Outlook.Inspector
Dim wdDoc As Object
Dim oRng As Object
Dim sCase As String, sRef As String
sCase = InputBox("Enter the case number")
sRef = InputBox("Enter the reference number")
With olItem
.BodyFormat = olFormatHTML
Set olInsp = .GetInspector
Set wdDoc = olInsp.WordEditor
Set oRng = wdDoc.Range
oRng.collapse 1
oRng.Text = "++++++++++++++++ Admin use only ++++++++++++++++++++" & vbCr & vbCr & _
"Case: " & sCase & vbCr & "Reference: " & sRef & vbCr & vbCr & _
"++++++++++++++++++++++++++++++++++++++++++++++++++" & vbCr & vbCr
oRng.collapse 0
oRng.Select
End With
lbl_Exit:
Set olInsp = Nothing
Set wdDoc = Nothing
Set oRng = Nothing
Exit Sub
End Sub