I have the same system block mentioned earlier where system privileges won't allow me to use Application.COMAddIns(Name).Connect = True. This is a bit of a workaround, but to get the COM add ins box to pop up you can use SendKeys to pull it up. Keep in mind that SendKeys only excutes at the end of a run on Excel 2010 onwards, so to get it working correctly you would need to check if the user is connected to the add-in first thing. If so, call another sub; if not use SendKeys to get the dialog open and end the sub. These are the keystrokes that worked for me, there may need to be some edits depending on how many options are in your menus.
Sub test()
'Checks if COM is installed and active
comFound = False
comRibbon = True
For i = 1 To Application.COMAddIns.Count
If Application.COMAddIns(i).Description = "NAME" Then
comFound = True
If Application.COMAddIns(i).Connect = False Then
comRibbon = False
End If
Exit For
End If
Next i
'Exits sub if not installed
If comFound = False Then
MsgBox ("You do not have NAME installed.")
Exit Sub
End If
'Directs user to rest of code if active, otherwise opens dialog
If comRibbon = True Then
Call test2
Else
MsgBox ("Please select NAME in the following dialog before rerunning.")
End If
SendKeys "%FT{DOWN}{DOWN}{DOWN}{DOWN}{DOWN}{DOWN}{DOWN}{DOWN}{TAB}{TAB}{TAB}{DOWN}{DOWN}{TAB}~", True
End Sub
Sub test2()
'Rest of code
End Sub