Can the supplier declare a lower value on the customs invoice?

It happens constantly and it is fraud in every major market. The consequences fall mainly on the importer of record, not the Chinese factory: undervaluation can trigger penalties calculated on the duty evaded, seizure of the goods, and in serious or repeated cases criminal exposure. It also destroys your ability to claim properly if the shipment is lost or damaged, because the insured and declared value is the low one. A supplier who volunteers to under-declare is telling you they are willing to break one rule on your behalf, which is information worth acting on.