The simple answer is yes. In order to be a good tennis player you need to be able to move quick enough to the ball and then be able to balance and make good contact with the ball on your racquet and hit it back to the spot your want. Some of the attributes players should have are explosive power, strength, speed, flexibility and agility, they will also need aerobic and anaerobic endurance.
I believe a good exercise regime off the court will greatly compliment you on the tennis court. Once you have solid technique you need the athleticism to be able to perform those shots under pressure or stress and the fitness to last a match.
Most points last between anywhere between a couple of seconds to 10 seconds but demand a high amount of intensity and quick movements but the match could last up to 3 hours. I believe your training program off the court should involve exercises that would simulate what you are trying to achieve in a tennis match. Some of the following would help - plyometrics, skipping, fast footwork, core exercises, balance exercises like yoga and pilates, and overall strength work.
Just remember that tennis players probably on move 3 or 4 metres at the most in one direction so long distance running maybe good for your overall fitness but I am not sure that it will be as beneficial for your conditioning or explosive power.