Presumably if they weren't brought back as a separate force their role would just fold back into the Navy. Back then the Marines primary duties were shipboard security, prevention of mutinies, to act as boarding parties, assisting with cannons during naval battles, raiding/assualting shore defenses, etc. Most of this would just fall back to the Navy and sailors would be trained in those same roles. Basically, they'd be marines and not Marines, as naval infantry would still be needed.
Down the road a bit once amphibious invasions/assaults come into play those roles would likely be carried out by the Army just like in Europe in WWII (though the Marines did train them there), and naval infantry becomes something more like SEALs or the Royal Marines. Maybe the job of amphibious invasions becomes specialized divisions of the Army the same as 10th Mountain and 82nd Airborne are specialized units.
