When I put the SSH key inside
authorized_keys for root, can I SSH in to the server as a different user without having the
authorized_keys for that user?
No, you can't. Each user (including root) has their own
Each user has their own .ssh folder with auth keys. However, you can achieve (what I think you are trying to do) by going to the first server and typing the command.
ssh-copy-id email@example.com enter your password once.
your key is copied to that user now.
repeat for other users that you need to connect as. e.g.$ ssh-copy-id firstname.lastname@example.org