I agree Think sport specific if you can run the bases all the hell out and fast then thats prob the most running at anyone time that you would ever need. Best to focus on sprinting etc.
Will lots of running effect leg strength SURE depends on how much but lots of longer range running will have an impact and you will need to structure training around it for recovery etc.
Do cardio after weights or on your off days to avoid overtraining your body for pitching. 20 to 30 mins of moderate cardio is fine, such as eliptical, walk on treadmill w/ a high incline, jump rope, or light jogging for time. Sprints are a whole new issue and I’m not very well versed in sprint training.