Does an invitee need to approve an invite to a 1:1 or group messaging channel?

By default, this is not needed. When a user gets invited into a Group Channel, the user automatically becomes a member of the channel.
We have a setting that can change this behavior.
At the application level, you can change auto accept to true(default)/false.

At the user preference level, you can change auto accept to true(default)/false.