Yup, that's how the nhra approved box I have is setup. You drill a hole into the box, grommet it, and pop a hole in the floor. This box was $60 but it comes with a metal hold down and the like. I used to have my battery tray bolted to the floor with the stock hold-downs on it, then a walmart marine box and strap, and decided since I have my kids in the car, it should be more robust.
But I don't think that marine battery box truly seals the entire box, so it's just venting to the trunk space, and you'd need to seal it for a tube to outside to do any good.