Purpose of using that after comma

I personally think that this comma is intended to prepare the reader for a coming explanation of what has just been said:

If you answered yes, (and by answering yes I mean your answer) that you do intend to pursue need-based financial aid, then you will receive an award letter.

This additional information could also be put between parentheses:

If you answered yes (that you intend to pursue need-based financial aid), then you will receive an award letter.