If your drawer unit is solidly built and not too heavy, it’s fine to leave the contents in the drawers.
If the drawer unit is solid and heavy or if the unit is kit-set and not solidly built, it is better to empty the drawers. Heavy furniture is not easy to move and much more prone to damage and home assembled furniture does not transport well – especially when drawers are full.
The men may need to put the unit on its side to move or transport it. If they do, they will probably remove the drawers and re-insert them later.
Tip — Clothes travel well in plastic sacks. Sacks are less expensive than boxes and are easy to load in the truck. “If in doubt take it all out”