We investigate an atomic ensemble of interacting bosons trapped in a symmetric double-well potential in contact with a single tightly trapped ion which has been recently proposed [R. Gerritsma, Phys. Rev. Lett. 109, 080402 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.080402] as a source of entanglement between a Bose-Einstein condensate and an ion. Compared to the previous study, the present work aims at performing a detailed and accurate many-body analysis of such a combined atomic quantum system by means of the ab initio multiconfiguration time-dependent Hartree method for bosons, which allows us to take into account all correlations in the system. The analysis elucidates the importance of quantum correlations in the bosonic ensemble and reveals that entanglement generation between an ion and a condensate is indeed possible, as previously predicted. Moreover, we provide an intuitive picture of the impact of the correlations on the out-of-equilibrium dynamics by employing a natural orbital analysis which we show to be indeed experimentally verifiable.