I have never printed ship models, but I see no particular issue in doing this. For 3D printing, especially for FDM type, it is not important what model you are printing (a cube, a boat, a dragon, a dog, an automotive prototype functional part, etc), what is important is that the design of the part to be made in such a way that it would be printable on a 3D printer (my main concern would be thin walls).
As for buying your own 3D printer, I am encourageing everyone to do this. It is a fun hobby (sometimes annoying). The Prusa i3 Mk3 looks like one of the best FDM 3D printer on the market (except for the high end industrial and professional 3D printers that start at 25.000 euro and can go up to 200.000 euro). I actually intend to purchase one in the near future (the Prusa i3 Mk3, not the big expensive printers).
Please see the first picture of one of my finished products (450mm long, see the 300mm ruler in the picture for dimensional reference). The part on top is done from 2 components glued togher. The assembly line is hidden (I present it in the second picture) and the part is finished and painted.
As I said I am working now on a 1000mm model, it is actually the exact same model, scalled up. Please see the 3rd picture with some of the sections printed and in comparison to the original 450mm model. I should be able to have the final part (assembled, finished and painted) in this weekend and I will post another picture if you are interested.
If I can help you with anything else, please let me know.