Yes, if you dont want to take it outside the engine and generate custom collisions thats one way.
Another, preserving the drawer space so things can be dropped in, would be to create custom boxes to follow along with the normal woodplanks that make up a drawer.
5 rectangle hulls are all you technically need.
And yes, its less performant than a single box, and it is less performant than 1 convex hull. But if you have 2/3 convex hull the boxes may out do it.
(Then again this is academic at best. Unless you have a scene in a futurama like file room with billions of drawers, you do what you need for gameplay. Not for performance).