If you go under general anesthesia , without a muscle relaxer.. would you still need an artificial airway ?

It is possible: Anytime somone undergoes general anesthesia, there is a moderate to high probability that the airway can become compromised requiring artificial ventilation. Some procedures can be done under moderate sedation in which the airway reflexes are usually preserved, but full general anesthesia usually requires some form of airway management

Absolutely!: No anesthesiologist in their right mind would put you under general anesthesia without securing your airway. Muscle relaxants aren't the only thing keeping you from breathing. Opiods (morphine), sedatives (Versed), and anesthetics themselves (IV Propofol, Sevoflorane gas) all reduce central drive to breathe and are given together as a cocktail. Don't end up like Michael Jackson.

Not necessarily,: there are quick cases where a mask only will be used, also if you have loose teeth an LMA might cause them to be dislodged and tracheal intubation might be difficult or not desired. A mask only is more difficult for the anesthesiologist.

Anesthesia airway: Typically under general anesthesia you will need some airway to prevent the tissues in your throat from collapsing and blocking your breathing. The decision depends on the surgery and your medical history. Generally if you are not being given muscle relaxants they will use what is called an LMA or laryngeal mask airway. It is much easier to place and less traumatic than a breathing tube.