Charlie,
No, at best, the resolution will stay the same, but the distance between pixels could be smaller if you make the picture smaller.
Think of resolution as the amount of information the picture contains - a good example is a roman mosaic picture, made up of lots of small tiles. When you take your digital pic, if your camera has 2 million pixels, you've got 2 million tiles to use for your picture. (Hence the 1400 x 1400 approximation I mentioned earlier, which assumes a square format).
If you make your picture smaller, you either need to use smaller tiles (increase the dpi.) or use fewer tiles. There's no point using resolution which is beyond the eye's limit of resolution, you just need to use enough to make a 'good enough for your needs' picture.
Your printer will be the best guy to ask about what resolution you need and he should be able to show you samples of work at various resolutions. I find 600 dpi pretty good, but I don't know what your expectations are .
So you'll reduce picture resolution if you reduce the size of the picture but keep the dpi value the same .
Hope that helps, good luck.
Regards,
Graham