Damage due to operating system removed from disc

Wiping the OS won't damage the machine, but it might make it difficult to restore the Mac to working for the next user.

FYI, this is what should have been done: What to do before you sell, give away, or trade in your Mac - Apple Support

If the Mac was otherwise prepped properly, then step 7 should get it back to working, partly depending on the age of the Mac.

What you need to do before selling a Mac:

What to do before you sell, give away, or trade in your Mac - Apple Support

After you download the OS, do NOT install it, just turn it off. That way, the buyer will see the welcome screen and can set it up using their own Apple ID.