You could do it but you'd barely be getting into backcountry at all.
The Old Bridle Path marks the border of the state park, and is also on a narrow ridge (park on the west and cliffs on the right), for most of its length - there's a short section outside the park where it first makes a northward turn to climb the ridge, but that's already getting steep.
There's a section, low on Falling Waters, along Dry Brook where you'd be outside the park and the slope isn't too bad. In fact the woods there are pretty pleasant and open if I recall correctly. But you're still only about half a mile from the highway as the crow flies, and you'll probably hear hikers passing by at all hours. Might as well camp at Lafayette Place and hike with less gear.