Excuse the nitpick, but what you meant to say is "All those scripts having #!/bin/bash at the top, they will still work exactly as they always have
if you change the line to read #!/bin/zsh"... and it's not quite clear why you would want to do that if the script is already working as intended, hence this clarification.
Of course, a script that has #!/bin/bash at the top will keep working regardless of which shell you execute it on anyway, even a shell with a completely different syntax such as tcsh, because that shebang line will tell the OS to always use bash to execute the script--no matter what shell you're using to invoke the script.
It's different when you source a script (usually done using the eponymous shell built-in) since then the shebang line will be treated as a comment and ignored, and all other lines in the script will be executed in the context of the current shell.