I was thinking about basing the character concept around the D&D 3.5 Ninja class, which does provide some cool non combat skills and abilities that would be perfect for stealth and burglary (like the ability to turn invisible for example, or some bonuses to skills like like jump, climb etc.) The question is: Do oriental classes like the Ninja work in Eberron, and would you allow it in your game?
In theory, Eberron is supposed to contain absolutely everything that's in any official 3.5 sourcebook. In practice, this isn't always true, but it works for the Ninja.
The Player's Guide to Eberron (p.81) gives two possibilities for ninjas. First, it states that the Dhakaani Empire (an ancient empire of goblins and hobgoblins overthrown 5,000 years ago by the extraplanar invasion of the Daelkyr) had a ninja tradition. If you want to emphasize the oriental aspect, you'd probably want to go this route.
If you're interested in the stealth and burglary more than the oriental flavor, though, ninjas are also associated with the Mark of Shadow, a dragonmark which provides stealth-related abilities. The Mark is associated with the elven Houses of Phiarlan and Thuranni, organizations concerned with spying and intelligence-gathering (though in theory, they're the "Entertainer's Guild") who split in 972 YK. If you go that route, you could choose to join one of the houses, which gives you a built-in role in the world and motivation. Or you could choose to be a freelancer or go-between between the two sides.
So the answer is yes, I would most certainly allow it. If you want more information on Thuranni and Phiarlan , see p.152-4, p.348-51, p.354-56 of the free Grand History of Eberron linked to above. More information on the Dhakaani is on p.36-9, 40-43 for history, and p.146-151 for the state of goblins and hobgoblins in the setting's present.
EDIT: Just saw JohnnyJohn's post. If both of you were accepted, somehow I think you'd cross paths a lot.
But to answer your question, that could certainly be interesting. Write something up.