I found the following post that is related to what I am trying to look into with GF.
http://www.gravityhelp.com/forums/topic/only-one-submission-per-forms
I modified my post after doing some more research here. In addition to the above functionality, which looks great to block users from submitting more than one form from the IP they are at (though would be nice if it was cookie based), I would need the following:
On a page, perhaps a user "member area" page, there would be a notification that they have submitted a particular form. - This means that a user, upon submitting, would get a notification that they have completed a form by email (default functionality), but also a text based notification (might be programmatic, but where to start?) on a particular "member page" that says "Hey, you completed Task 1. Move on to Task 2." Something like that. Thoughts?