If you have emission inspection in your area, it will, lol. You would have to take ALL 5 CATS off to really make a difference. The 3.0 Ranger uses a multi-stage cat system for efficiency and minimum backpressure. There are 2 "preheat" cats on each branch of the Y-pipe that do some conversion and keep the exhaust gas hot before the main cat. 2+2+1=5 cats.
In '01, you have a catalyst efficiency monitor that reads the oxygen both pre-cat and after the cat and determines if they are working properly. If you remove the cat/cats you will have a constant check engine light.
It's illegal under federal law and I believe most state laws to alter the emission system by removing the cats. If you don't have state emission inspections then you may never be caught -- but it's something to think about.
But it doesn't hurt anything but the air we breath -- which isn't a great idea. You'll find some people on the boards who will tear you a new you-know-what for taking your cats off, lol.
Overall, I'd say don't do it unless your truck spends most of it's life offroad or racing.