Can you be a good PM and have no experience programming?!

Welcome to devRant! If you understand a devs perspective - and hanging out on devRant will give you that - I believe you could. I was a PM for years but I also had many years of dev experience in my favor.
If you want to be a PM and are in the US I strongly suggest you get your PMP certification.

Yeah, a really good PM doesn't need to know much about the details of the project, they should just need to know how to run a project and make it move forward. The tech stuff should be left to the architect and or devs. A good PM can run ANY project, because a project is a project no matter what it produces.
That said, the symbiosis from great cooperation between a PM and a architect can be really great for a dev project.

even a PM was a developer, he/she might not be a good PM too..., so vice versa