With Acrobat Reader DC, I was able to press NVDA+Space on the first edit field to go into Focus Mode, type my first name in the field, then tab through and hear all other fields. I didn't bother filling them out.
I didn't examine the form in detail, but there appear to be ten unlabeled checkboxes at the end. If I had examined those in browse Mode, I may have been able to determine what they were fore, but I did not hear that as I tabbed through them.

But, yes, I was able to hear the names of and fill in edit fields as I tabbed.

I also tried Jaws, and the overall experience was smoother, but I am also more familiar with that screenreader.

So yes, I am quite confident I would be able to fill out that form and email it back.
Chris