This could be achieved by using the COM interface into Domino from the ASP page. It would require that a Notes client be installed on the server however, as the ability to initialize a session is based on the Notes ID referenced in the Notes.INI on the server running the script (it can be Domino server as well – just so you know). Also, the ID has to have access to every Mail database you will access.
Another option is to reverse your plans, export it to SQL first (I would use the DECS product to do this, or something like it anyway) – then use ASP to pull it from SQL instead. Might be easier.