In my IP2003 experience I've only been able to attain silent form submit through instantiating an Outlook object and then building the email using Outlook scripting.
I think any other way you can think of to submit from within IP will require user interaction.
As it is, it sounds like your user is going to have an awkward experience anyway - they are on a webpage, push a button, Infopath opens (assuming they have it) a form appears, does something to pre-populate values, and then they have to hit another button to submit it.
Maybe consider leaving Infopath application out of the equation and just populate an XML document using webpage scripting (create an MSXML DOM) and send it using webpage scripting/button? The XML document can be a blank Infopath form.xml. That way the recipient can open it by double clicking and see it in Infopath.