Not exactly. {, }, [, ], (, ) are not part of the English alphabet but they are widely used. Same thing for ->, =>, !=. But things like λ are not used at all. So the alphabet of computing is ASCII.
You are supposed to be able to type them if you write in English. Also, if you are in polite company, it's alright to drop the occasional Greek word. So here we are: if you can fully write in English, you can use all these characters.
Ascii-only is the modern equivalent of all-caps. Something archaic, still used by old people with hopelessly limited input devices.