  We establish a class of sufficient conditions, ensuring that a sequence of
multiple integrals with respect to a free Poisson measure converges to a
semicircular limit. We use this result to construct a set of explicit
counterexamples, showing that the transfer principle between classical and free
Brownian motions (recently proved by Kemp, Nourdin, Peccati and Speicher
(2012)) does not extend to the framework of Poisson measures. Our
counterexamples implicitly use kernels appearing in the classical theory of
random geometric graphs. Several new results of independent interest are
obtained as necessary steps in our analysis, in particular: (i) a
multiplication formula for free Poisson multiple integrals, (ii) diagram
formulae and spectral bounds for these objects, and (iii) a counterexample to
the general universality of the Gaussian Wiener chaos in a classical setting.
