It's possible, but the culture is not conducive to it. According to Simon Singh's book on the subject, Wiles had to go as far as stockpiling several years' worth of conference papers in advance in unrelated areas so he could submit one occasionally while he was really working on FLT, just to affect the appearance of productivity. He also taught a phony graduate course in which his main collaborator enrolled and most of the other students dropped out, just so they could use the class time to thrash out some of the details.