There's no problems whatsoever with having it all hooked together. It won't harm the converter any; it just basically shuts off if the voltage it senses exceeds its setpoint, such as when the alternator is supplying power.
It would be the same as if you had a solar installation. Rather than the power coming form solar cells, it comes from the alternator; however, it's all the same so far as the converter is concerned. Similarly, you could also hook up a second converter or a 12V battery charger if you for some reason wanted or needed to.
It probably goes without saying, but this is emphatically not the case for AC circuits. Different AC sources can be out of phase with each other, and cause tremendous currents and associated very bad effects if connected together in parallel. That's one reason why it's absolutely essential to have some sort of a transfer switching arrangement between a generator and shore power connection. (Generators that can be paired together, such as Honda inverter generators, have special circuitry built into them to synchronize their outputs.)