Can a Mortgagee obtain a certification from its sponsored Third-Party Originator (TPO) that Quality Control was performed for the TPO's FHA-insured Mortgages?

No.  Mortgagees cannot accept a certification from a sponsored Third-Party Originator (TPO) to satisfy FHA’s Quality Control Program requirements related to sponsored TPOs and Mortgages originated by the sponsored TPOs. 
For additional information see Handbook 4000.1 I.A.6.k and V.A.2.b.ii available at:

All policy information contained in this knowledge base article is based upon the referenced HUD policy document. Any lending or insuring decisions should adhere to the specific information contained in that underlying policy document.

Topic Number: KA-03400