You can. So long as you don't mind slight increase in image fuzziness and a significant increase in exposure times.
Originally Posted by aaronmichael
Two things make the image on a pinhole camera fuzzy: the size of the pinhole, and the effects of diffraction, the bending of light around an edge. But only the light that 'touches' the circumference of the pinhole will be diffracted. In both cases (i.e. short camera, long camera), the same amount of light is being diffracted (i.e. bent slightly outward radially). That bent light will spread out as it heads toward the film, increasing the overall fuzziness of the image. On a longer camera, it has a longer path in which it can spread out before it hits the film. So you may find that your images will be less sharp on the longer focal length camera, even with the same pinhole. And, you'll still have to pay the price of longer exposure times.
So, you could make yourself a bigger pinhole and shorten your exposure times. True, you'll increase the fuzziness due to the size of the pinhole. But you'll decrease the fuzziness due to diffraction. However the net fuzziness will probably be higher.
And if you really want to get technical, even in the bigger pinhole, the total amount of light being diffracted (i.e. bent or scattered) will increase, but the proportion will be less. And so it's relative contribution to image fuzziness will be less.