There’s no reason why you can’t drink ground coffee without filtering it first as the coffee grounds are edible, but you’ll likely get a much grittier beverage. In some parts of the world, it’s common practice to brew unfiltered coffee, such as the “cowboy coffee” from Turkey, where the coffee grounds and water are boiled together.
However, the jury’s still out as to whether it is healthier to drink filtered or unfiltered coffee. If in doubt, do some research or check with your doctor before you embrace unfiltered ground coffee.