It is - but I don't see the issue.
Your signature has a bit of sense though - but Sky2 will continue to exist with the fact that it squeezes the last bit of revenue from their archive.
I only pointed that out because Sky normally updates their logos within weeks/months of them changing. But then again, Sky are doing this elsewhere on their sites and also in the past on various channels.
As for my signature, I'm very aware that they will keep Sky 2 on air for quite a while as an archive channel (Mainly former/current Sky 1 shows). My only complaint really is that Sky 2 rebrands with new idents and breakbumpers as it has not had a major refresh since 2011. Seeing it is an archive channel, however, I doubt Sky will
Seriously, just do us all a favour and close Sky 2..