What you're actually asking is: Would I hire a "programmer" without a degree and with zero work professional programming experience on their resume.

Yes. But only if that programmer had a good portfolio and showed a lot of promise. They'd have to interview well and be able to explain what their code does and why. Oh, and I'd only ever hire them as a junior developer, which of course means that the company has to be willing to handle that situation.

Once they've had a few jobs, the experience portion completely replaces the need for a degree and the question is obviously 'yes'. The rest of the interview is much easier for someone with actual experience, degree or not.