Keith, If you access a document from the documents collection, instead of using the active document, AND make sure not to do anything to the screen (regen, redraw, zoom) it should work. For example, this works:
Sub test()
Dim AcadApp As AcadApplication 'Object
Dim acadDoc As AcadDocument
Dim dblPt1(2) As Double
Dim dblPt2(2) As Double
Dim dblpt3(2) As Double
dblPt2(1) = 100
dblpt3(0) = 100: dblpt3(1) = 100
Set AcadApp = GetAcadObject
Set acadDoc = AcadApp.Documents.Add("acad.dwt")
AcadApp.Visible = False
acadDoc.SaveAs ("c:\test")
acadDoc.ModelSpace.AddLine dblPt1, dblPt2
acadDoc.ModelSpace.AddLine dblPt2, dblpt3
acadDoc.ModelSpace.AddLine dblpt3, dblPt1
acadDoc.Save
AcadApp.Quit
Set AcadApp = Nothing
End Sub
Another way would be to use ObjectDBX through the AcadObject since it never opens a drawing for editing anyway.