No, You May Not Roll on Items for Another Class and Strip Out the Mods

I would also argue from the perspective of the game designers that by design certain pieces of gear are intended for certain classes through appearance, not only stats, though they may be used by others. The primary function served by this is that of silhouetting, or making player characters distinctly distinguishable on the battlefield. It was a very important design decision to the team that worked on Warhammer: Age of Reckoning, and it is common knowledge that part of that team was tapped for the design of SWTOR as well. Does that mean that nobody else should ever use a piece of gear designed for class X? No. The designers' intention does not mandate the use, but instead only strongly suggests it.

So if the silhouetting of particular characters is important, then what if an Agent wants to be silhouetted as a Marauder? Does an Agent have a lesser right to look like a Marauder, especially if the Marauder in the group already looks like a Marauder?

"wants" being the operative word here

So if the silhouetting of particular characters is important, then what if an Agent wants to be silhouetted as a Marauder? Does an Agent have a lesser right to look like a Marauder, especially if the Marauder in the group already looks like a Marauder?

If the designers are making a special point to have a certain appearance, then needing for that particular appearance seems to gain validity.

If it is not a stat upgrade for the Marauder, should he roll greed on a "Super Awesome Marauder Suit" that drops?

Game mechanics question: Can you remove mods from gear without binding to them? If you win an orange piece of gear, can you take out whatever mods might upgrade someone else to give to them?

No. As soon as you modify an unbound item it and all of its mods become bound to you.

If the orange item were BoP to begin with, you wouldn't even need to modify it first for the binding to take effect.