Is it possible to create a Mac-Based Distro? ElemenataryOS is a linux distro.

But I like things like Hammerspoon. Is it possible to make an OSx distro? With custom stuff like custom apps installed?

Then I can re-install things quickly on all my OS devices.
Sure. Apple delivers the asr command which is called from the graphical Disk Utility to clone user data into a disk image. There are other tools like Carbon Copy Cloner and SuperDuper that do similar and extra tricks for backup and cloning. 

You can delete the user accounts and home folders and also remove the AppleSetupDone file to get a new system boot if you prefer that. 

As long as you’re running licensed macOS on hardware that’s correct for the version, imaging is something you can do. Others also automate tools like brew so you can dump on .dotfiles and install apps by recipe instead of by imaging. 

You will want to get a lawyer to read the license if you are distributing software as opposed to scripts or methods to automate things. Laws and licenses vary and most people need lawyers to know if local laws make licenses more or less effective. 

https://www.apple.com/legal/sla/