Installing MacOS via USB stick
Yes, you can create a bootable USB that can automatically install OS X. It would mimic the functionality of the Recovery Disk option when booting. Here's a link from Macworld about how to do it with the latest version of OS X, Sierra. It's less complicated than it sounds. When you start your Mac, hold down the option key to choose the USB drive that you've created.

http://www.macworld.com/article/3092900/macs/how-to-create-a-bootable-macos-sierra-installer-drive.html