I think you’ll find that even Emacs doesn’t really do C-x-d as if they can all be pressed in one sequence. Mashing all three keys at once is probably not going to do you any favors. However, viewed as a sequence, Sublime Text can do these things.
If you keys sequence reads:
"keys": ["ctrl+x", "d"]
Then if you press C-x then d (with no control modifier) you’ll get the sequence.
If you want to just keep holding Ctrl down, you could do:
"keys": ['ctrl+x", "ctrl+d"]
You will still need to lift your finger up from x to d though… you cannot literally do C-xd or something like that.
There does exist a good Emacs mimic mode in “Emacs Pro Essentials” which you can find on Package Control.