Don, when an athlete trains with weights does it throw off their game in whatever sport they may play? No. The training with additional weight provides them with greater control and precision over muscle movement and ability with whatever they may use to play. Using a heavy "training" deck is supposed to do the same thing. I don't think it throws anything off.
Your comparison isn't very apt - weight training in sports is for strength (or is the sport itself) while the practice of cardistry is a matter of precision hand movements and developing muscle memory. It's like taking a student calligrapher, teaching him to write with a very heavy pen, then after some months taking it away and giving him a lighter pen. For the first several days after the switch, that lighter pen will throw off his or her movements, requiring the retraining of their muscles and tendons to become accustomed to using less effort to make the same movements. I used to practice
aikido, and if I trained extensively with a heavy
bokken (practice sword) or
jo (a staff approx. four feet long - the distance from your armpit to the floor) and at my rank test had to switch to a lighter model, it would take away some of my precision in my
kata (basic moves, drills) because my body's muscles had built up their memory with the heavier weight.
You mentioned sports and athletes. Take any sport with a thrown ball. Have an athlete practice with a heavy version of that ball and set up a practice target that he or she can hit from a fixed distance. Have the athlete practice for maybe a half-year or a year. Then switch the heavy ball for a light one and tell the athlete to hit the exact same spot he or she was hitting before. Their ability to throw the ball won't be hindered since it's the same movements, but their precision would be hampered because the weight difference takes getting used to and the athlete will likely overshoot several times in the beginning until he or she becomes adjusted and retrains those muscles to apply less force at the same level of control.
It's why most ball-throwing or -kicking sports regulate the permissible composition, size and weight of the ball used in their sport. American baseball players LOVE Japanese baseballs. They contain a rubber core that allows for hitting the ball to a greater distance than they'd normally be able to using a US-regulation baseball. Which is why MLB never permits their use, just as they don't allow larger, smaller, lighter or heavier balls that are beyond their specifications. All the players practice on equal footing using in essence the same tools of the trade.