Does macOS Sierra support Server Side Copy via SMB and/or AFP?
Unfortunately, the source code of the AFP driver is not free software, so it's difficult to give a definitive answer on that. However, it appears that Netatalk supports copyfile, so it's likely that the answer to that question is yes.
If you look at the source code of the latest version of the macOS smbfs driver, you can see that it does implement the copyfile operation (see smbfs_vnop_copyfile)

According to the release notes, OS X did that since ca. 2013:


  8) Added Server Side Copies (OS X SMB Client &lt;-> OS X/Windows SMB File
  Server)


Whether that actually gets used with FreeNAS, I cannot tell - I have no access to a FreeNAS system.