I think it is do-able, I have read diet plans where people do it, very very tough though. If you are just doing it for weight loss purposes its kind of hooey. In most studies a well controlled vegan diet outperforms low/no carb diets every time. The reason you lose alot of weight really quickly when you go keto is that you run out of glycogen in your body which is hydrophilic aka it attracts water. So when you run out of glycogen and go keto your body dumps a ton of water. Thats why most people who go keto gain back almost all of the weight instantly when they come back off it.
If you are crazy keen on fast weight loss in a ketogenic form, there is the velocity diet. Which is essentially you drink 5 protein shakes/day (easily made protein) and then have 1 full meal a week. You do it for a month I believe? and you lose a ton of weight but you feel like hell (one guys gums started bleeding like crazy), but if you are in a rush. I have lost 25 lbs in 7 weeks before just by reducing calories and increasing activity, without dying.
That was a lot in there, hope that helps