Once I realized that leaving the Xbox on standby meant auto updates on everything, I changed that setting right quick (to "power saving", meaning truly off when I turn it off). That was about 2 years ago. There are no issues with playing the Xbox or Minecraft without updating, except of course, you have to play offline. If you want to play with friends online, you need to have both your system and the game fully updated. That's necessary, in technical reality; it isn't just MS or 4J being overly restrictive. Different versions of system software and game code are not going to get along together very well.
So, in short, yes, you can play Minecraft on the X1 without updating it, but only offline. First, switch your power mode to "power saving". When you go launch MC, it may tell you that it needs an update. If you don't want it, cancel out of launching the game, go into Settings->All Settings->Network, and tick "Go offline". Now launch MC again, and it will work.
Edit: Wow, this thread is 2 months old. I'll leave the reply here, for whoever may find it useful. But I assume the OP already found his answer elsewhere.