The short answer is NO. Over the years I have had a number of coworkers who were actually very good programmers but did not have degrees. One in particular worked for Microsoft and wrote hardware device drivers. Another acquaintance merely formatted reports and wrote simple mainframe JCL.
The fact of the matter is that a majority of programming work is trivial and akin to laying brick after brick. Only and small minority of programmers make decisions like implementing algorithms or computing high level math functions… It’s mostly mundane and ordinary.