I've been using the DT 770 80 Ohm as "gaming" headphones for over a year. I still have the Custom one pro but for games à la CoD, these are clearly better. However, the DT 770 is connected via a PCI-E Soundblaster.

This is a headphone for professional applications in the field of sound engineering. It is intended to be operated via an audio interface. The sound reproduction is "frequency-referenced". In other words: If you don't need the thing for mixing, you'd better leave it alone, otherwise you'll be terribly disappointed by the untapped frequency band. For a bit of pretty audio, there are much cheaper and more hi-fi headphones. (Gaming headsets)
These headphones do not amplify the input signal. So the question has to be reversed, "does your Xbox controller amplify enough?"
I tested it, it works for me. I would still advise against it.