Best practices for syncing two Macs using Sierra
I am going to try answering per question, except the first two. So here goes my 5p: 


  
  Am I correct that this setup will work as intended?
  Will syncing of one user continue to run in the background if a second user logs in to the same machine? (Presumably not if the 1st
  user logs out, but what if they stay logged in while the second
  account becomes active?)
  


Yes, for both. 

Also in addition, for best practices and keep each user's file separate, create the Documents, Pictures, etc folders inside and iCloud Drive. Now ask each child to put all their stuff in that folder. 

If did not do that, it will still be stored inside the local machines' ~/Users/ folder. 


  If I link all the accounts on both computers to iCloud, will I end up with duplicate copies of files that currently reside on both machines? Or will the syncing process recognize when two files are copies of one another?


Do you mean using the Auto upload feature? 


  Would it be better to upgrade one machine, link all of the accounts on that machine to iCloud, then do a clean install on the second machine and create &amp; sync new accounts on that machine to iCloud?


If you are moving all of User1's docs to their iCloud Drive, it does not matter. 


  If I notice that files don't seem to be syncing automatically is there
  a way to force a sync?


Not that I know of