We study the AB(2) "dimmer-connector" chain within a generalized Hubbard model, which contains site-dependent parameters, and different chemical potentials for A and B sites. Considering one electron per atom, we carry out exact calculations for finite clusters, and derive some asymptotic results, valid for macroscopic chains We take a non-vanishing intra-dimmer electron hopping, thus departing from the condition of a bipartite lattice In spite of that, the system persists ferrimagnetic in some region of the parameter space, thus generalizing a theorem of Lieb for bipartite lattices A somewhat surprising result is that the ferrimagnetic phase is possible, even for a very large chemical potential jump between A and B sites In another respect, we show that a previously reported macroscopic (2(N)) degenerancy of the AB(2) Heisenberg chain ground state (GS) is fully removed on going to the (more fundamental) Hubbard model, yielding a non-magnetic GS.