Directly to your question: yes, it is more than possible to do it. You do it via AutoCAD COM automation. That is, you run your application (in your case, it is VBA code in Access), which automates AutoCAD (either starts a new AutoCAD instance, or find a running AutoCAD instance), makes AutoCAD open drawings, update/retrieve data to/from drawings...
However, before you do this, you really need to ask yourself/users: do you want to run 2 apps (Access UI and AutoCAD) in order to achieve the business goal? Since AutoCAD has to run anyway, can the business goal be reached withing AutoCAD (i.e. only writing AutoCAD VBA code)?
Anyway, if you have decided to use another application to control AutoCAD (be it Access, or Excel, or anything else for that mater), following VBA code would let you connected to AutoCAD and do something with it (hopefully you do know AutoCAD well and know very basic AutoCAD COM object model; otherwise, you need to do quite some study before you can do anything meaningful with AutoCAD):
Sub DoSomethingWithAcad()
Dim cadApp As AcadApplication
Dim dwg As AcadDocument
On Error Resume Next
Set cadApp = GetObject(, "AutoCAD.Application")
If Err.Number<>0 Then
Set cadApp = CreateApplication("AutoCAD.Application")
End If
If cadApp Is Nothing Then
MsgBox "Cannot connect to/start AutoCAD." & vbCrlf & _
"Something is wrong with the computer!"
Exit Sub
End If
On Error GoTo 0
Set dwg = cadApp.Open ("[drawing file path/name]")
DoSomethingWithDrawing dwg
dwg.Close True/False '' Close the drawing with or without saving changes
End Sub
Private Sub DoSomethingWithDrawing(dwg As AcadDocument)
''You access drawing data here
'' You can also update drawing here
End Sub
Of course, in your app (Access/Excel/...) the VBA project must set reference to AutoCAD type library.