The TSB does not mention the Evap System Monitor, and the evap system isn't related to the three monitors mentioned in the TSB, so I doubt that doing the TSB fix will address the Evap System Monitor not promoting to Ready status. The evap system is checking for fuel vapor leaks, while the TSB addresses three monitors that check for exhaust emissions system issues (catalytic converter performance and O2 sensor performance).
That said, I haven't myself confirmed, nor have I seen any other forum user confirm, that the TSB does or does not address Evap System Monitor readiness, so I'm only making an educated guess here.
Also, in some states, you can pass emissions with a single Monitor with a status of "not ready." So, if you do the TSB and fix the emissions readiness issue, you may be able to pass without the Evap System Monitor ready.
Yes, both cleared. Monitor EVAP Not Ready and Monitor Heated O2 Not Ready
joe