In SQL Server, is it possible to have a PRIMARY KEY on a table without either CLUSTERED or NONCLUSTERED indexes on the same key?
In short, no. A primary key by definition requires uniqueness, an index on the primary key field is the database engines route to enforcing this constraint.

From BOL:


  When you specify a PRIMARY KEY constraint for a table, the Database
  Engine enforces data uniqueness by creating a unique index for the
  primary key columns. This index also permits fast access to data when
  the primary key is used in queries. Therefore, the primary keys that
  are chosen must follow the rules for creating unique indexes.