If you meant right at the terminus, that's not really safe to do. Or particularly necessary at that exact point, but YES, you should get a DBR/Odo pic once you pass beyond the end of the Interstate in Wilmington. From the E2E rules page
HERE;
Rules: It is your responsibility to prove the ride. The IBA “gold standard” of verification is the DBR at the start, along the route as necessary, and at the finish location.
Satellite tracking displayed on a SpotWalla trip map is required for the Interstate End to End series. It is your responsibility to ensure the satellite tracking functions well enough to demonstrate you remained on the primary Interstate route. Using the DBR or satellite tracking device OK or Custom marker at key locations may be necessary. When in doubt, mark it; when really in doubt, get a DBR.
It continues on and tells you:
For most of these rides, you must ride the entirety of the selected Interstate from and to its opposite endpoint coordinates.
You must obtain a DBR in each of the two endpoint cities, ideally before the geographical beginning and beyond the ending of the Interstate, traveling through the coordinates shown above.
Based upon that, you should document the end with a DBR in Wilmington, NC. Note that while the Shell off Gordon Rd at X420 does have a Wilmington address, I would suggest you go to the Mobile on Ringo Dr since it is past the terminus whereas the Shell is before it and the rules specifically call for "beyond the ending of the Interstate". There is also a Costco with an ATM and gas station just past Ringo Dr if you're a Costco member and the timing works for you.
(made an edit to add clarity)
