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Welcome to FTE! You will find a lot of useful information here.
If you intend on running an exhaust with no cats or mufflers, yes, you can. But it is going to sound like crap. I would recomend getting rid of the cat(s) and using a Flowmaster, or other similar chambered muffler to give it a good tone.
The important question is do you have emissions testing in your area. If you do, you are going to need the cat to pass. If that is the case, you could try running a cat and no muffler and see how that sounds.
You can do anything you want.. the only real technical requirement for correct engine operation is that the O2 sensor be installed in the exhaust close to the original location and connected.
This Hennessey Takes the Expedition Tremor's Off-Roading Capability to the Next Level
Slideshow: The VelociRaptor Expedition gains a lift, upgraded suspension, Brembo brakes, and trail-ready equipment while retaining the stock 440-horsepower EcoBoost V6.
Rezvani's Latest Post-Apocalyptic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.