Not that I am aware long term. Short term maybe, depending on what the diet and general health was before.

Short term urination could increase or be more frequent as the body gets rid of excess water. Carbohydrates tend to hold on to water in the body. When a person cuts back on carbohydrates some of the very first weight lost will be water loss. People report their swollen ankles going away and people who are on diuretics probably should talk to their doctor as the prescription may need to be adjusted lower or eliminated. But that is usually only in the first couple weeks.

Once the body settles in to the new normal I don't see why there would be any difference.

However excess salt consumption will cause more urination because the body closely regulates the amount of sodium in the bloodstream. It will get rid of any extra through the kidneys and urination.

The loss of fluid early on is what causes the so called keto flu, which is not flu at all. It just has some of the symptoms of flu and is due to an electrolyte imbalance. Usually self correcting within a couple weeks or many people cure it by just taking some salt or an electrolyte mix with salt, magnesium and potassium. The kidneys adjust to the new normal, whatever it is. But it may take a week or two. 

Keep in mind this is coming from a high school educated (that actually graduated) (edit: add retired) dirt farmer. Not a nutritionists or doctor. Probably foolish to pay any attention to what I say.