Catalytic converter and Turbo....Question !

Hi,
In gas cars, I know you can hollow the cat converter (did this as a student when I couldnt afford to buy a new one...replaced it later though !). I gained minimal power from it. I was wondering if the turbodiesel engines need the backpressure generated by the cat in order to perform, or would I potentially gain a horsepower or two from having the cat hollowed ??? BTW, I am not thinking of doing it, as I dont even have my car yet, its only theoratical !
Thanks,
J-F