The endpoint for posting users does not say anything about sending confirmation emails to users when you create their account. If I were to use the post users endpoint as a register screen, will this send the confirmation email? Or if not, is there some way I can do this?
There isn't anything in the API for sending email confirmations. Creating a user in the API is equivalent to creating a user via the control panel which is generally a different flow than a standard user registration (and doesn't ever send email confirmations).