Yes, but, if you are applying "Z" units of energy to a process without a catalyst  and a catalyst is now added which, lets say 4 folds the reaction, in the above process "X", do you not have to be reducing the HO bond to produce that result..??..
I agree the energy to produce the "Cat" has to be added, but if the "Cat" is a true "Cat", then it doesn't partake in the reaction. Depending on the longevity of the "Cat", its initial energy used for creation could be miniscule comparing to the liberated energy of the reaction.