If you have some way to stir the old sand and filter it with something like a Magnum I think it would be a good idea to do so. That would remove a lot of the detritus and other stuff trapped in the sand. I think a lot of nutrients get released during a tank move from this source. If you can minimize it, more the better.

I also run the sand through some really big plastic collanders to remove all the snail shells and other larger stuff that accumulates in the sand bed.