Would it work if I covered the landing gear bays with paper and painted over them to give it a flying appearance?

ZzZGuy is correct that most models give you the option, but quite often the undercarriage doors don't exactly fit the wheel bay openings. First thing to do is to test fit the doors that came with the kit. If they fit then use them, you might have to glue supports inside the wells, at the correct depth, to leave the doors flush once fitted. If the doors do not fit then, before you glue the wing halves together, trace through the gear door opening, onto plastic card and cut them out. You still might need to trim and add supports.
Now I'm guessing that you have probably already built this kit? If so try this; lay low tac, see through masking tape (Scotch tape or 3m are 2 types) across the gear bay openings. Make sure that the pieces overlap each other. take a knife with a sharp blade and, carefully run it around the gear opening, cutting the shape out in the tape as you go. Lay this masking tape gear door onto plastic card and cut the card out. Scribe any detail into the card and fit. You may still need to add supports.
Hope this helps.
Mal