I would say it depends on the specific role and project, but for most people who write code, likely not.

Coming from a mechanical engineering background, I understood "engineering" as the application of science for problem solving - or, put simply, applied science. Some examples:

1. When a civil engineer applies solid mechanics to select a cross beam. 2. When an electrical engineer applies E&M to design a circuit. 3. When a mechanical engineer applies heat transfer to analyze cooling patterns on a laptop.

Under this definition, most "SWE" work isn't engineering - if anything, it's closer to applied math and logic?

That said, definitions are only useful inasmuch as they allow us to make sense of the world and communicate with others, so I'm not sure this is the most useful question