The statistics of many-particle energy levels of a finite two-dimensional system of interacting electrons is studied numerically. It is shown that the statistics of these levels undergoes a Poisson-to-Wigner crossover as the strength of the disorder is decreased. This crossover occurs at a similar strength of disorder to the one-electron delocalization crossover in a finite two-dimensional system and develops almost simultaneously at all energies. We interpret this crossover in terms of delocalization in the space of occupation numbers of strongly bound and compact electron-hole pairs (excitons).