I want the InviteBox widget to show, not as a button or with any text, but instead I want to imbed it into my wordpress site. Can I do this?

Absolutely. Click on the "Integration" tab and select "No button” (embed widget directly into the host page).  Then  paste the integration script where you want the widget to appear on your site.  Note:  If you are using the InviteBox WordPress plugin, disable it first.