I have done that actually: I told ChatGPT that it should pretend that I'm a Bash terminal and that I will run its answers verbatim in the shell and then respond with the output. Then I gave it a task ("Do I have access to the internet?" etc.) and it successfully pinged e.g. Google. Another time, though, it tried to use awscli to see whether it could reach AWS. I responded with the outout "aws: command not found", to which it reacted with "apt install awscli" and then continued the original task.
I also gave it some coding exercises. ("Please use shell commands to read & manipulate files.")
Overall, it went okay. Sometimes it was even surprisingly good. Would I want to rely on it, though? Certainly not.
In any case, this approach is very much limited by the maximum input buffer size ChatGPT can digest (a real issue, given how much some commands output on stdout), and by the fact that it will forget the original prompt after a while.