Firstly, contrary to the popular belief, being the Devil's number is 666, is not true. The actual number is 616. But yes, there is a connection.
Yes, there is a lost of connection overall. Even with 666 and 616. Six Wings, Six spikes, Six Stipes and Six Legs. Giratina has a lot of 6's. The Giratina Description also says "Renegade Pokemon." Meaning it is somewhat evil, and is made to be a kind of Dark Beast Shadow. The point of your question though is true. Pokemon and GAMEFREAK designed Giratina as a Devil, so your observations are correct.