I doubt it. Their gut flora would grow appropriately to maximize the digestion or whatever foods they are finding. The nutritional differences in various animal sources vary enough even within one species based on what it's fed that the original composition of a wild T-Rex diet would be similarly varied in both macronutrient and micronutrient composition. Without a direct and toxic or physical problem with mammal consumption, they should grow and breed well on modern animals. Much in the way introduced predators like bullfrogs thrive on whatever the heck is running around.
Even today, you can feed animals pseudo-foods like pellets made of corn and soy and they often are able to survive and breed in spite of it. Swapping out a diet of giant lizards for a diet of mammals isn't nearly as big a change as a dog has to make, born to eat everything from rabbits to raccoons to deer, but instead captively offered toxic corn pellets, and still surviving to adulthood.
Even today, you can feed animals pseudo-foods like pellets made of corn and soy and they often are able to survive and breed in spite of it. Swapping out a diet of giant lizards for a diet of mammals isn't nearly as big a change as a dog has to make, born to eat everything from rabbits to raccoons to deer, but instead captively offered toxic corn pellets, and still surviving to adulthood.