Products formed when solid CuCN is dissolved in aqueous KCN solution
No, both $\ce{[Cu(CN)3]^2-}$  and $\ce{[Cu(CN)4]^3-}$ species are formed. According to Wikipedia article of copper cyanide:


  ... but rapidly dissolves in solutions containing $\ce{CN−}$ to form
  $\ce{[Cu(CN)3]^2-}$ and $\ce{[Cu(CN)4]^3-}$, which exhibit trigonal
  planar and tetrahedral coordination geometry, respectively. These
  complexes contrast with those of silver and gold cyanides, which form
  $\ce{[M(CN)2]−}$ ions in solution.The coordination polymer
  $\ce{KCu(CN)2}$ contains $\ce{[Cu(CN)2]−}$ units, which link together
  forming helical anionic chains.


See this paper for more details.