Yea you can do it. You have to cross the river at McIndoe Falls (west of Monroe) If you look at this map find Littleton NH. take trail 10 west to Monroe, then cross the river at McIndoe Falls. That would be an awesome trip.
If you get a map for you GPS from Backwoods GPS Trails, It would show all the fuel, hotels, restaurant, etc. accessible from the trail. You could plan it out good with it.
http://backwoodsgpstrails.com/SledMap/SledMap_J_E.html