can I update generation 2 Apple TV on my Mac?

Apple TV (2nd generation), A1378 from 2010, had its last version system software v6.2.1, released in September 2014. Later updates are not for this model.

You don’t

• The few ‘apps’ that it still has, should work.
• AirPlay may be very limited, as content providers may require a later model as minimum for the receiving device.
• Signing in may require some hoops.
• Some iCloud functionality may not work anymore.