They do take PSs. I am not sure how often it is necessary but I do know when I made one for our last trip, Disney Dining could not make it for me but gave me the direct # to call. When I called, I was able to make a PS but was warned that it would only be held for 5 minutes as a very large convention was starting that day. Well, it was huge. Shortly after we were seated, the restaurant was full.
For our upcoming trip, Disney Dining was able to make our reservations for Fresh. I currently have 3 mornings scheduled there although I will probably change one. But it was that good.