The sail panels will be fine, however you may have to deal with them popping out of the lip that hold them down from time to time. You might also be putting extra presure on the stiching, leading to extra "wear". One alternative that will reduce to noise is this:
(Note: the add says that it's not compatable with the unlimited top because of the plastic panels. You can unzip the sail panels and remove the plastic pieces, then it will work. I took the plastic pieces out a year ago, makes dropping the top easier and I've noticed no difference with them in or out.)
As to the sunrider, I never got the straps so I've been using it without them for 2 1/2 years. Never had a problem.