Yes, you should always make sure to completely empty out dressers, desks, drawers, and anything else holding your personal effects.
This is important because not only does having stuff inside the dressers make them quite a bit heavier for whoever is moving them, but it can also pose a danger if the drawers slide and things inside shift around, potentially falling out.
The majority of movers won’t move dressers or cabinets that have stuff inside of them, so be sure you go through and empty everything out of all of your dressers, drawers, and cabinets well ahead of moving day.