HAM failovers and other autonomous operations are triggered when host side HDLM multipathing detects an I/O timeout or link down to the arrays. In the case of an HDLM upgrade or ESX upgrade, the arrays are static and are up, and do not take any action simply because a host logs out of the target port (unless the upgrade is "sloppy" and there are greater than 1000 errors in a 6 minute period, in which case it will trigger a horctakeover, but this behavior may be attentuated by enabling HMO 48, which will cause the arrays to ignore the high error count from the hosts).
So in summary the upgrade should have no impact to HAM. The HDLM User Guide makes no mention of HDLM requirements in the event of an ESX upgrade. Assuming you are upgrading to a version of ESX that is supported by the HDLM VIB, the maintenance mode and reboot should not require any special steps for HDLM or HAM.
If there is an ungraceful disconnect (live ESX is suddenly shutdown or cable disconnected) then a reservation may be orphaned on the datastore, which may require manual intervention (rebooting the host that owns the reserve).
If you do encounter a problem during the upgrade:
1) STOP. Do not take any further action.
2) CALL US: +1 800 446-0744 or Int +1 858 547-4526
3) Be ready to give us the serial numbers of the arrays (so we can check them in Hi-Track), the version of HDLM and the verison of ESX, and a detailed description of the problem including any screen captures if possible (a picture says a thousand words).