Can a spinal disc issue at c6/c7 induce pain that mimicks wartenberg's syndrome in the wrist, and cause nerve pain in the elbow (like when straightening out the arm)?

No, this misconstrues different concepts. Unless the disc compresses the C7 nerve root, there will be no radiating symptoms in the arm. If there is radiculopathy, there will be numbness over dorsal hand and extension weakness, but no specific localized sensory radial issue, otherwise. Straightening at elbow suggests more of a tendinitis, as weakness of extensors do not equal pain per se.