Your idea $\ce{C = A + B}$ changes the order of reaction, and has no physical basis.
The product of two concentrations, $\ce{c_{a}}$ and $\ce{c_{b}}$ in the equation $${\partial c_\ce{AB} \over \partial t} = -k_\mathrm{off} c_\ce{AB} + k_\mathrm{on} c_\ce{A} c_\ce{B}$$ has the physical interpretation of $\ce{A}$ and $\ce{B}$ must collide for reaction to occur, and is hence a second order reaction.
Your proposed solution would change that to first order in a fictional component, $\ce{C}$, and leads you astray.
You also forgot to include the other reactions for the bimolecular case: $${\partial c_\ce{A} \over \partial t} = {\partial c_\ce{B} \over \partial t} = k_\mathrm{off} c_\ce{AB} - k_\mathrm{on} c_\ce{A} c_\ce{B}$$
As an aside, little k is a reaction constant. Equilibria are described with big K. It is unclear what $\ce{k_{d}}$ means in your question.