Eric - there are a few forest roads along the MST that allow dispersed hiking, they just aren't very well-known and can be difficult to get to. The dispersed hiking area promoted the most is just down the road from Black Mountain Campground - I guess it kind of works as a free overflow for tent campers.
Anyway, I received an interesting email from trail maintenance list that I'm on in regards to GSMNP. I'm sure this pretty much applies to all national parks, so I will share in verbatim:
"If congress fails to settle the budget issues by Friday night the government will shut down. If that happens the Park would get the word sometime Saturday morning and would then shut down the Park. The “word” has to come down through channels including the OMB so it may not be fast.
The Park has asked us to notify all our volunteers that even if they can access the park during a shutdown, they are not encouraging folks to use the park during that time.
This is for two reasons (1) In the event that someone is hurt, the Park will have greatly diminished ability to respond with SAR and EMS (2) Once the government shuts down, VIP agreements become void. Thus, if someone is working in the park during the shutdown and gets hurt, he or she will not be covered under workman's comp.
Recreational hikers should also be aware of the situation. Most gates will be locked, including the one at the Greenbrier Range Residence. But it may take some time to get the gates locked. If you were already hiking in Porters Creek when the gate were locked at the Ranger station you would be trapped in. Emergency gate openings for trapped vehicles would be handled as best they could.
You can monitor the national news tonight and get a feel for what to expect, but if congress settles things it may not be until midnight, as you undoubtedly know."