The Email Opt Out field in Luminate CRM will only update Luminate Online in the constituent is being unsubscribed.  A constituent can only be opted in to site-wide email by this option being manually updated within LO.  

If you opt someone out in LCRM  (by marking the Email Opt Out box on a contact record) it will sync to LO and opt the constituent out of email. Accept Email will be set to No, however the opt-out date will not be populated in LO. An interaction of type Email Opt-Out will be logged in LO.

You cannot opt-in constituents through an update in LCRM. If you opt someone in via LCRM (by un-marking the Email Opt Out box) it will NOT sync to LO. No change will be made to the Accept Email field. No interaction will be logged. The constituent will continue to be opted out of site-wide email within LO.