So let me preface this by saying I am relatively inexperienced in the adobe products. The fan noise is pretty loud and in a small enclosed area I am not sure that it would be usable with no mic or the flex mic. It definitely demands attention so if you are wanting to film a wedding or something where you want to be an unnoticed person. I would say it is not an option for those types of situations. When I tried to remove the noise in post (using Audio Effects>EQ), the fan noise was on the same frequency as child's voice. If I am doing that wrong then someone please correct me.
Someone who can probably weigh in a little more here is @damoncooper. I believe he has this setup with a wireless mic.