Nurture streams will send on fixed dates. For instance, if and email is sent on May 8, the next casts will be on May 15th, May 22nd, May 29th, ...
You would twist it to do you what you want to do, but sincerely a standard smart campaign with a filled out form trigger, and 7 days waits will be much simpler.
That's the same conclusion I came to as well.
I would use a regular trigger campaign for this. Although if you use the engagement engine you will get the dashboard to see how well each email is being engaged with