I agree with Doug 100%. You must have a sealing compound of some kind. Pumbers putty is best used on vit. china or a stainless steel sink. 100% silicone caulk should be used on cultured marble tops because of the oils in the putty. The oils will break down the gel-coat on marble and discolor the area around the drain in time.
If you don't use a sealer on the installation of a lavatory drain, it won't hold water when you try to fill up the sink. The stopper may hold, but the water will leak between the chrome and the surface of the sink and run down the drain. The rubber gasket underneith the sink may prevent it from leaking into the cabinet or on the floor, but you won't be able to hold water in the sink bowl.
If you don't use a sealant on a kitchen sink strainer, the water will simply run under the sink and onto the floor. The sealant forms a gasket that seals the strainer to the sink and prevents leaking. I typically (after thirty years) have found silicone is one of the best sealants. Though some plumbers sill use puddy. Its all a matter of preference.