First, Outlook does not prevent you from mass emailing. 

Second, OnyakTech Mail Merge for DNN doesn't have anything to do with the outbound email in Microsoft Outlook.  I know that may not make sense, but OnyakTech Mail Merge collects data from your web site and then passes it Outlook with the email content you specify.  Outlook handles all email processing.

So to answer your question....  No, OnyakTech Mail Merge can not handle the situation you have put forward.  It is not a messaging server,  it doesn't handle MX records, etc.

That is something you need to handle on your own or with your network administrator.  Microsoft Outlook can handle multiple email accounts and OnyakTech Mail Merge uses the active account.... so you can send emails using any account you have setup in Outlook.

If your web site hosting provider limits your connection on port 25, then you may want to consider changing your MX record to point to a Microsoft Exchange hosting provider.  Or... setup your own exchange server and change your MX record.

Hosting providers are usually slow at processing email and may put limitations on you to prevent bottlenecks in their network.   So it is always better to have a dedicated email server or at least an email provider.

There are a LOT of Exchange Server providers out there that only charge $20 a month.  Includes all kinds of features and they are always fast and secure.