Why there isn't any unimolecular addition reaction?
The problem I see with your question is that you mix up two completely different concepts. The first concept is the reaction order (i.e. order of the kinetics, for example unimolecular = first order) which is dependent on the number of components that take part in the rate determining step of the reaction. The other concept is the type of the reaction, e.g. addition, substitution, functional group interconversion.

Naturally, most addition reactions will be of the type $\mathrm{A + B \rightarrow C}$ or something like that, but that neither means that they will be of second order kinetically, nor that all addition reactions are of that type. Intramolecular additions would be one example for a unimolecular addition.

Please be careful though not to mix up the order of the reaction and the stoichiometry of the written down reaction.

Imagine a reaction were you have $\mathrm{A+B \rightarrow C}$ and $\mathrm{B}$ is used as the solvent, so that $\mathrm{B}$ is available in large excess. While there are clearly two components needed for the addition to proceed it will appear to be unimolecular (first order reaction).

Strictly speaking, the stoichiometry of the reaction has nothing to do with the reaction order. 

However, most addition reactions can be conceptualized to be of the form $\mathrm{A+B \longrightarrow C}$ whether that means that $\mathrm{A}$ and $\mathrm{B}$ are part of the same molecule or different chemical entities or if the rate law will actually appear to be of second order as well then depends on the specific case.

In that regard, I don't really see the point in asking whether an addition reaction might be unimolecular, as the kinetics will depend on the specifics of the reaction while the stoichiometry can be inferred just by looking at the equation. I hope that clearifies it.