Had the full freeway not been delayed for 40 years, would it still have been designated Interstate 885? 285 was approved in 2005, 485 was approved in 1991, and 685 was only approved last year.
I'm guessing that it would not have gotten a route number. The original plan was a spine between downtown Raleigh -and- downtown Durham, with a spur around the southwest side of Raleigh and a spur around the east side of Durham. The three sections that were built became the Wade Avenue Freeway, the Tom Bradshaw Freeway (I-40) and the Durham Freeway (originally all NC-147), and the East End Connector got postponed (over-and-over-and-over...). (For the record, the western portion of the Tom Bradshaw got renamed as the Dan K. Moore Freeway in 1985).
The Wade Avenue Freeway didn't get completed inside the Beltline and never got a route number (probably to discourage Durham folks from using this as the main route into downtown). Similarly, the East End Connector would have dumped onto Miami Boulevard/US-70 Bypass which would have continued to I-85 as a fourlane highway. It probably wouldn't have gotten a separate route number for a similar reason (to discourage Raleigh folks from using the EEC as a bypass of Durham).