You absolutely will be intubated while under general anesthesia and will be monitored the entire time by the anesthesiologist who puts you under; that is their entire role during your surgery.
While you may be tired and a little groggy, you will not be discharged while still under anesthesia; that completely dissipates while you're in post-op recovery.
As Anomalia said above, if you're staying over night at the hospital, they'll tell you to bring your machine (if you're actually diagnoses with sleep apnea following your sleep study).
If you're having your surgery as an outpatient, you should use your machine while you're resting the first couple of days because you definitely will sleep. After that, just use it as you normally would.