I've seen those good at writing get better at it after getting into programming. Also, I've seen some learn or begin to write sufficiently well after they've been programmers for a while.
Yes, of course. I consider myself good at both. Both practices have the same foundation, at least in my case: organized thought and the concise & illustrative expression of complex ideas. When I am writing or programming, my mental experience of the activity feels the same, like the same parts of my brain are working during both.
I feel likewise.
Is there a phrase used in programming communities that is similar to writer's block?
In programming, is it more a logic block than a block based on fear, such as "writer's block"?
I think it's more a logic block. When I experience it, sometimes my subconscious helps me unblock it while my body continues to sleep :)
walking away from the problem...sleep, shower, some activity that flushes the mind, is a great way to overcome a block, be it programming or creative.