Well, theoretically, but practically speaking, no.
To be in ketosis you need to limit your carbohydrates to typically around 50 g per day. A typical diet might be 1500 calories, 40 g carbohydrates, 75 g protein, and a whopping 115 g fat. But I’ll tweak things a little to make it more possible.
A serving of lettuce might have 2 g, a serving of broccoli 5 g, a slice of bread or large piece of fruit 15 g. (These are very round numbers.) So to maximize your calories/carb ratio you eat 8 cups of broccoli and you’re at 50 g carbs, 250 calories, 20 g of protein and all your carbs but almost no fat.
At this point some people might point out that the broccoli is almost all fiber and that fiber doesn’t count. However fiber does count some because you can digest it partially. The exact amount is impossible to predict. You might very well be able to eat more than 8 cups of broccoli. In reality you aren’t eating 8 cups of anything anyhow, so I’m just going to ride with this example. YMMV.
First problem is you need more protein. All vegan protein sources contain carbohydrates and have a worse calorie/carb ratio than broccoli. Your only options are highly processed food like pea protein powder or soy protein isolate. You can meet your protein needs that way. So let’s add 3 big scoops of pea protein and now we’re at 53 carbs, 87 protein, 10 g fat, and 650 calories.
The rest is easy. 3/8 a cup of olive oil.
Okay, you will want to mix up the vegetables, try some nut oils, and you can mess with pea protein and textured vegetable protein. You will probably want to swap out some broccoli for some other foods like nuts, avocados, or real peas. But neither of those will supply enough protein or fat for you to avoid the processed protein and pure oil.
If there were some plant foods that had largish amounts of protein and fat but no carbs (aka meat) you could definitely pull it off. What you need are some foods that have 1500 calories but less than 50 g carbs to work with. But there are no unprocessed plant foods that meet that standard.