Yes, as long as you can achieve a complete gate set (over some N-qubit logical subspace) by arranging the atoms, and as long as the computation and read-out is

Yes, as long as you can achieve a complete gate set (over some N-qubit logical subspace) by arranging the atoms, and as long as the computation and read-out is reliable enough to get results, I think that's literally what it means to build a computer. (To formalize this, more needs to be said in terms of what the gate set is and how reliable it needs to be, but I think that's the basic idea.)