The FCOM does not state if the Oxygen gets mixed with ambient air or not
During your next emergency refresher, have a close look at a pax mask and figure out the airflow.
Adding to previous posts, while there are variations in detail design, the generic strategy is that the passenger is breathing from a (rebreather) bag into which the supplemental oxygen flow (via the tube from the oxygen supply), ambient air (either via holes or a simple valve arrangement), and expired air (from the lungs) are allowed to mix prior to the next breath. This is not a closed system, though, and there will be provision for the bulk of the expired air to pass to the outside of the bag.
So far as the smoke scenario is concerned, the bag is pretty useless and counterproductive. However, you can rip the bag off the hose, stick the hose up your nose and then cover your face with (preferably wet) clothing as a filter. For hoses which have an inline expiration check valve, the other option is to disconnect the hose from the valve (usually just a simple hose over spigot fit) and use the supply hose end up your nose .. this one depends how long the hose from the supply to the valve is.