cd without an argument will change directory to $HOME if $HOME is set and the value is non-empty as defined in the standard linked above. That’s not to say that all Unix-like systems do or even try to implement everything of that standard, but it’s a good indicator pointing to that a lot or most of them probably do.
As for cd ~, tilde expansion is done by the shell, not by cd. Same goes with any other command that you type ~ as the leading part of a path and provide as argument. (Also, in bash, among others, cd is a builtin command.) The shell will substitute the ~ for the path of your home dir when ~ is alone or followed by a slash and anything else. (And you probably know also that ~example would refer to the home dir of a user named “example”.)
I think you will sooner run into a system with a shell that doesn’t do tilde expansion, than you will run into a Unix system where plain cd without an argument doesn’t bring you to your home dir.
Technically the chances of tilde not working are the same as cd behaving differently because they’re both shell builtins.
I’m guessing (though admittedly not checked) that both ~ and cd (without parameters) are defined in POSIX. In which case any edge case that doesn’t conform could reasonably be discounted with regards to the submission’s exercise.
