'sup, Tar! Welcome to the deep, dark world of joining in and commenting on this Discord 
Anyways…
I totally agree that it would be a cool and awesome-sounding idea. Maybe even useful? But “feasible” isn’t a word I would use lightly.
Like everyone else said, Norfolk Southern owns those tracks. Since transit corridors that aren’t for cars are not public utilities (read: citizens get to call dibs) in the U.S., neither the federal or state government can demand public transit to be allowed through. That makes those tracks private property, so you can’t really do much as long as NS isn’t willing to hear you out about passenger rail service on their turf -and history suggests they’ll hate your guts for mouthing those words anywhere near their face.
This means you’re left to beg NS to let trains pass through that 1.2 miles (1.9 km)-long path -and for you to come up with a convincing reason to believe you.
Remember, we’re struggling to justify a Durham-Raleigh commuter rail line or light rail of any sort in the Triangle. In light of that, I’m not sure if this would be a battle worth fighting…
PS 1: a possible compromise would be to lobby for a Dix station to be part of a Raleigh-Fayetteville rail route, which is being studied by several government agencies right now. …but there’s a whole other thread for that.
PS 2: about public transit being 'controversial'...
The affordable housing discussion is hella controversial, since it ends up being a bloodbath of arguments which are all well-thought-out and relatively watertight.
I don’t think the discussion about public transit fits the bill -or at least, not on this site. I think most of the discussions are repeats of the same, core arguments of “oooh this sounds really cool you guys!!” versus “wait this doesn’t pass the b.s. sniff test”. But at the end of the day, there’s a pretty good consensus that some sort of comprehensive public transit investment would be an investment that’s worth the effort; a lot of us seem to be on the same page, on that end.