If the code is running on the client machine you can iterate the
Outlook.Application.COMAddIns collection. That has all addins. You can
locate yours and reference it. This little snippet assumes using VB.NET, it
would be different using C#:

' In Connect class:

Private addInInstance As Office.COMAddIn = Nothing

' In OnConnection() event handler

addInInstance = TryCast(addInInst, Office.COMAddIn)
addInInstance.Object = Me ' critical setting

' Public Sub that can be called from outside the addin
Public Sub CalledFromOutside()
   ' do whatever you want
End Sub

Your external code that works with the Web service can then get your COM
addin from the Outlook.Application.COMAddIns collection and use code like
this to call that CalledFromOutside() method:

Dim myAddin As Office.COMAddIn = olApp.COMAddIns.Item("myAddin.Connect")
If (myAddin IsNot Nothing) Then
   myAddin.Object.CalledFromOutside()
End If

That CalledFromOutside() method can take arguments like a flag or whatever.