Not worth the risk. As others have noted, no lateral stability. Even if you're confident in not getting injured I personally don't like the feel of running shoes for tennis. Too high up off the ground. Any sports requiring lateral movement I prefer less cushioning and being lower to the ground.
I always wear sports specific shoes. It may sound expensive to buy different shoes for different sports but really if you wore just one type of shoe you would wear it out more frequently than if you had 2 pairs. So you're just spreading the wear between the different shoes and they last longer.