Further investigation, suggested by Navarro and Vento, is carried out for a non-relativistic hybrid quark model with extra pion degrees of freedom. An effective adiabatic approximation for the solution of the dynamical equations describing common dynamics of quarks and pions is studied. This technique allows us to construct two-body quark-quark potentials including the gluon and pion exchange process and confinement effects. In the framework of the Faddeev equations formalism, the three-body problem is solved, and in terms of the exact wave function the main static characteristics of nucleon and delta-isobar are calculated. We also analyze relative contributions of pion effects and relativistic corrections. On the basis of the exact solution of the three-body problem, the inadequacies of the model under discussion are pointed out.