Does your console BASIC run on the RPI Zero W1?
I've no idea, I don't have one. I don't make available a pre-compiled version for that platform, so you'd need to recompile it from the source code. I'd be interested to learn what happens if you try.
As regards dependencies, it does rely on compiler extensions and intrinsics supported only by GCC and Clang, but that's not a major limitation in practice.
But the fact that it can successfully be run on the Raspberry Pi Pico, which is little more than a microcontroller, shows that the demands on system resources are not great.