Yes, the ESSecureBrowser required by Examity apparently works just fine on Mac OS Big Sur, including new Macs on the M1 chip.
Most of the (unnecessary) worry about this issue has stemmed from two main factors:
1) The official system requirements for the ESSecureBrowser only indicate support for Mac OS 10.14.2 Mojave through 10.15.1 Catalina, and prior to the exam, both GMAC and Examity had ignored customer emails inquiring about this potential compatibility issue.
2)
There is no way to run the ESSecureBrowser in order to test it beforehand. This is a secure design feature, but it also has caused a ton of consternation on behalf of users who try to run it and don't succeed, and then worry (again, unnecessarily) that their OS is incompatible.

Source:
https://www.mba.com/frequently-asked-qu ... question12Despite these potential red flags, I have now heard of Mac users successfully taking the enhanced GMAT online on Mac operating systems as old as High Sierra 10.13.3, and as new as Big Sur 11.4.