Strictly speaking, no. But I believe the number of people who can be sufficiently productive without formal training is not as high as you’d be led to believe. Programming little things is not hard, and that entices many people into the field without the real prerequisites to contribute effectively. Basically, if you don’t get formal training, you’re an amateur. You may be able to convincingly play a professional even if you are not. And software imposes a peculiar set of standards, making its far more likely for an amateur to pass themselves off as a pro.
Note, too, that there’s a difference between no formal training an no degree.