No, the constraint can require exactly one column. PostgreSQL even has an optimized builtin function for this, `num_nonnulls`.

In a recent feature I had an object field modelled as:

      type Destination = Customer of Customer | Supplier of Supplier | Warehouse of Warehouse

and the table representation was

      customer_id uuid null
    , supplier_id uuid null
    , warehouse_id uuid null
    , constraint unique_destination check (num_nonnulls(customer_id, supplier_id, warehouse_id) = 1)

It's not first class support, but manageable enough.