Can an old Apple TV Model A1427 be updated?

That would be a 3rd gen, which is still receiving updates (albeit basic firmware). The latest would be version 7.5

Be aware that the support mainly comes down to a version of the TV app that is available for that model. It does not actually run apps, so new services like Disney's will not be present, and existing provider have also been dropping support (the latest being HBO).

Hello,

I am sorry, this model cannot be updated any further.