Answer: No. Code 69436 doesn't include anesthesia services. The anesthesiologist should bill his own code for that according to the time the patient was anesthetized.
The inclusion of -general anesthesia- in 69436's descriptor is meant to differentiate it from tympanostomy not requiring general anesthesia. For office-based tympanostomy using local or topical anesthesia, the appropriate code is 69433 (Tympanostomy [requiring insertion of ventilating tube], local or topical anesthesia). When a physician performs tympanostomy in an operating room using general anesthesia, you instead report 69436.