no reason you shouldn't be able to. it's not considered a state park, which is CC only. the only thing you're not allowed to do, as far as i know, is operate a motor vehicle. people ride bikes, go horseback riding, and a host of other activities.
here's a interesting factoid: many of the scenes from The Road were filmed on the Abandoned Turnpike. you can go and pretend you're hiding from cannibals when you go.
i want to go out there myself to walk it. make sure you take pics and post them here.