Can a physician assistant be an anesthetist?

Yes they can but very few do. The majority of PAs working in the field have gone through one of the few Master's programs that focus on the discipline. Once working, the PA's title will usually be Physician Assistant Anesthetist.

Pay is similar to a Certified Registered Nurse Anesthetist (CRNA) or slightly higher. Job duties are similar except for the fact that more authority can be granted to a Physician Assistant Anesthetist because he works under the medical model under the supervision of a anesthesiologist. Any tasks which the doctor feels the PA is qualified to do can be delegated. This flexibility is not present with a CRNA who's work sphere is somewhat limited by established protocols.

One downside to being a Physician Assistant Anesthetist is that the position is only recognized in a handful of states which limits where the PA can practice in the field.

Good info about a PAA: http://paanesthesiaworld.us/

Most well known PAA educational program: http://www.med.emory.edu/education/aa_program/