Is there an instrument departure procedure or minimum performance gradient in the absence of a published standard instrument departure?
Yes, the required obstacle clearance is based on this minimum performance:


Cross the departure end of the runway (DER) at at least 35ft AGL (that's above the DER, not above the airport reference elevation)
Climb to 400ft above the DER before turning
Maintain a climb of at least 200ft per nautical mile (FPNM) until reaching minimum IFR altitude


The minimum IFR altitude is 1000ft above obstacles, or 2000ft in mountainous areas.

This is explained in detail in Chapter 1 of the FAA Instrument Procedures Handbook (starting on page 1-14). The FAA carries out an assessment to see if the airport needs a specific procedure (ODP or SID) and if it doesn't then the standard clearance performance above applies:


  If an aircraft may  turn in any direction from a runway within the
  limits of the  assessment area and remain clear of obstacles that
  runway  passes what is called a diverse departure assessment, and  no
  ODP is published.