Do refurbished MacBooks have their operating system re-installed?
When MacBooks get refurbished, their hard drive is erased of all data, then their operating system is reinstalled.
A refurbished MacBook is ready for use with a clean copy of Mac OS X or macOS, as a brand new model would be. Once you get your refurbished MacBook, you will be able to set it up as new or restore your settings from a backup of your previous MacBook.
We have curated an article to further make the doubts on refurbished MacBook clear. It tells you what are the pros and cons of using one.