Although an anesthesiologist would be the definitive source, I think it highly UNLIKELY that the use of the term Gas to refer to Anesthesiology is an acronym.
For one, it is not capitalized, ie GAS.
Two, most hospitals do not have Anesthesia "services" (ie, the S in GAS). There is a department, which would make the acronym GAD or AD, since much of anesthesia is not "general" but local or regional.
Three, anesthetic gases have a long history. Ether, the first one used, was the harbinger of the modern era of surgery and anesthesia. Now more commonly used gases are sevoflurane, isoflurane, etc.
Anesthesiologists give several drugs when adminstering anesthesia: an anxiolytic (often given in pre-op; has some nice amnestic properties) inhaled gases may be given to induce anesthesia (often used in children or needle phobic adults so the IV can be placed after they are asleep) and to intubate, and then the general anesthesia which may be a combination of gases, oxygen, muscle relaxants and narcotics. The combination of drugs used may depend on what operation is being done and the patient's needs.