Except for a couple of specifically designed units, no it’s not waterproof.
Most modern bathroom furniture is made in a similar way to kitchen cabinets, an MDF core which is wrapped with a laminate or similar, finishing product. This creates a surface that water can sit on but should not be left on for any length of time.
Many units have points where water can ingress, usually the same points where they join to the wall or basin, these need to be sealed with a waterproof sealant upon installation. If they are not, and water is left standing around these areas, then water will be absorbed by the core material and expand over time.
This is true for any modern bathroom furniture and care should be taken when maintaining them.
We do have a range of furniture made from an entirely waterproof composite material for when this is an issue.
If you have any questions related to this, please give us a call or jump on live chat.