I'm not exactly sure what you are asking...but the first thing I would check into if I were you is what kind of emmisions regs you have. If you have to have the truck smogged and have it inspected, then you will need to keep the cat on there.
To help clarify your question, there are two basic types of exhaust systems...turbo back and cat-back.
The cat-back system is simply from the catalytic converter back. It only replaces the pipes and muffler after the converter.
The turbo back system has a replacement down pipe and can either retain the cat or delete it...depending on the system you buy.
If you want to go more---remember it is illeagal to remove the imissions equipment---then you get to the off-road systems or a cat test pipe. I'm not saying that many don't do so, it's jsut something that you need to decide for yourself.
The cat test pipe is a pipe that will bolt into the place of the cat. Some may require an aftermarket system, although I am pretty sure that I have seen where some people have put them on otherwise stock exhausts.
The offroad systems on the other hand, remove the cat with no provision to reinstall it.
Now to answer your question the best I understand it, yes, you could remove the rear section of the exhaust, including the cat, and run it like that. There are quite a few with no muffler at all out there. I like mine turned out to the side, but an underbody dump would also work.
Straight pipe usually does refer to an exhaust with no muffler or cat inline.
) on the stock piping. If you want more whistle cut out the muffler. Get the T409 SS versions to prevent future problems.
down I-64 for like 5 miles over 80+MPH, hitting 90+MPH at times the whole distance.....NO problems. 
