You sure can. Think of the bacteria and bioload as opposing sides on a balance scale. The liverock, sand other areas the can house bacteria on one side and the bioload (fish, inverts, etc) on the other side. In a well balanced and established system there is, well, balance. Both side of the scale are even; living things produce waste and the bacteria process it all through the nitrogen cycle. Sounds easy, right? Well, for the most part this is how it should work but there are always small issues that come up.
One thing I always do when planning a tank upgrade is add a few bags of biomedia (Matrix, bioballs) to my tank or sump a few weeks before the change over to make sure that I have all of the nitrifying bacteria I possible can. The biggest area of concern I would have in your situation is changing over the sandbed. That will stir up quite a bit of stuff and might throw a wrench in the process. I would start to vacuum the sandbed a few weeks before to get some of the crap out of it before you change things over. Now that I think about it, if I were you, I'd consider replacing the sand and using the old sand to "Seed" the new sandbed. New sand would throw off the bioload/bacteria balance of course but it might not be as risky as trying to move a whole sandbed.
Has anyone else had issues moving an entire sandbed during a tank upgrade? I've always used the "old" sand as seed and never had the experience of transferring over much.