In the PDF manual, search for Compatible Lenses.
It says: Auto extension rings (PK-series 11A, 12, or 13; PN-11. (D600, page 285).
Then a couple of pages following that is the INCOMPATIBLE list. From the D600 manual, it says:
Incompatible Accessories and Non-CPU Lenses
The following can NOT be used with the D600:
• TC-16AS AF teleconverter
• Non-AI lenses
• Lenses that require the AU-1 focusing unit
(400mm f/4.5, 600mm f/5.6, 800mm f/8,
1200mm f/11)
• Fisheye (6mm f/5.6, 7.5mm f/5.6, 8mm f/8,
OP 10mm f/5.6)
• 2.1cm f/4
• Extension Ring K2
• 180–600mm f/8 ED (serial numbers
174041–174180)
• 360–1200mm f/11 ED (serial numbers
174031–174127)
• 200–600mm f/9.5 (serial numbers 280001–
300490)
The E2 is not mentioned, but it is older, and there is no reason to imagine it has magic properties. The danger of non-AI lenses is that they can interfere and cause damage to the body, to new stuff like the electrical contacts added later.
Like for example, the BR-2 reversing ring, incompatible now, and Nikon created the newer BR-2A which will not cause damage to newer bodies.
Times change, all is not equal.