Motivated by an important recent experiment [Deng et al., Science 354, 1557 (2016)], we theoretically consider the interplay between Andreev and Majorana bound states in disorder-free quantum dot-nanowire semiconductor systems with proximity-induced superconductivity in the presence of spin-orbit coupling and Zeeman spin splitting (induced by an external magnetic field). The quantum dot induces Andreev bound states in the superconducting nanowire, which show complex behavior as a function of magnetic field and chemical potential, and the specific question is whether two such Andreev bound states can come together forming a robust zero-energy topological Majorana bound state. We find generically that the Andreev bound states indeed have a high probability of coalescing together producing near-zero-energy midgap states as Zeeman splitting and/or chemical potential are increased, but this mostly happens in the nontopological regime below the topological quantum phase transition, although there are situations where the Andreev bound states could indeed come together to form a zero-energy topological Majorana bound state. The two scenarios (two Andreev bound states coming together to form a nontopological almost-zero-energy Andreev bound state or to form a topological zero-energy Majorana bound state) are difficult to distinguish just by tunneling conductance spectroscopy, since they produce essentially the same tunneling transport signatures. We find that the "sticking together" propensity of Andreev bound states to produce an apparent stable zero-energy midgap state is generic in class D systems in the presence of superconductivity, spin-orbit coupling, and magnetic field, even in the absence of any disorder. We also find that the conductance associated with the coalesced zero-energy nontopological Andreev bound state is nonuniversal and could easily be 2e(2)/h, mimicking the quantized topological Majorana zerobias conductance value. We suggest experimental techniques for distinguishing between trivial and topological zero-bias conductance peaks arising from the coalescence of Andreev bound states.