Yes, it certainly can be a profitable business. But it takes time to build up the sales and the competition is fierce. The key is knowing how to optimize your sales while keeping your costs low. A distillery is a very capital intensive venture with a lot of up-front costs so it takes a few years to make a profit.
Some spirits such as vodka and gin can be sold soon after production for immediate cash flow while others, such as whiskey, require several years of aging.