In the First and Second Ages of Middle Earth, Sauron had the ability to change into an appealing form to Men and Elves. He could then deceive them, and used the name of Annatar. However, once he was on Numenor and the Island was destroyed, so was his fair form so he was subsequently trapped in his "hideous" form.
Since it is said that he was gaining much of his old strength back, would it have been possible for Sauron to regain the ability to appear fair to the peoples of Middle Earth again had he regained the ring from Frodo and Sam?