I used to work out 4 times per week and play pool for about 2 years straight. My workouts only consisted of weight training. I pushed myself extremely hard, using heavy weights and short sets. The last set in each muscle group would almost always be to failure.
If you start a regular program, for the first 2 weeks or so you will be very sore. But once your body gets accustomed to the workouts, the soreness will not be as bad. At that point it is just a way of life and should not affect pool.
When you change routines, the week of extreme soreness will probably return.
Now to pool, in all this time, I have only had one bad experience after a work out. I had just done my lower body and got in a game at my room on the way home from the gym. When I was in my pool stance, I could feel my legs trembling and felt unsteady. I learned my lesson and never played again when my legs were wobbly.
However, after an upper body workout, I never had a problem shooting pool. No matter how sore my arms were, it never seemed to affect my stroke.
In the long run, working out can only make you a better player. It probably won't enhance your stroke and shot making ability, but it will give you more stamina and endurance for those all night long sessions. We all know how bending over to take a shot for hours upon hours is hard on the body. The stronger you are, the longer you can play at your true speed.