How can I use Sparrow to send iCal e-mail notifications instead of Mail.app?
There is a solution to your issue but it requires a little AppleScript jiggery pokery.

Johan Bruning posted an AppleScript for this on GitHub. He's included instructions for installing it in the README which is also visible on the project's GitHub page.

In his blog post about the script he writes, "I am happy to report it works like a charm and my iCal now finally sends e-mails trough Sparrow."