Send PDFs Upon Submit?

Can I configure Gravity Forms so that a person can select multiple PDF documents they want sent to the email address they provide, and then those PDFs are sent automatically to them upon pressing the Submit button...while a copy of the request is sent to my client's email to know that the transaction took place?

If so, can you point me to where that configured?

No Rob, I haven't built the form because it's theoretical at the moment and I'm going to a client meeting soon...and the client will want to know if I can build this form.

It would not be a file upload field...it would be "I, as a prospective customer, want these three PDFs out the five your company lists," and upon "submit" those three PDFs would be emailed to me, the customer, based upon the email address I provided in the form.

It eliminates a customer filling out the form request for product specific sell-sheet PDFs, a sales person getting the request for those sell sheets and assembling the ones needed and emailing them out to the person who requested them. It eliminates the sales person getting involved at all...he or she simply gets an automatic notification that the request was made (which I know how to do). Does that make sense? Just want to check if/how Gravity Forms can do this.

@David I'm trying the example, but I cannot make it work. What do I have to do to attach a file that is stored in the URL http://www.mywebsite.com/docs/testing.txt

I've tried replacing all with this, but didn't work:

$attachments[] = "http://www.mywebsite.com/docs/testing.txt";
return $attachments;

Thanks in advance