(C)ould passengers of either color be able to be delivered to the town.
Yes. (Passengers essentially just need to be able to reach a destination in their respective color using only your network and/or the Red/Green network.)
Would (Nürnburg) become a town that is both Red and Green?
I'd say yes, this is completely analogous to when a station becomes connected to both Red and Green. You'd need to influence both Red and Green to build out from Nürnburg, when both companies are connected to the city.