But of course, and in terms of connecting the two NPs and following the crest of the Blue Ridge, and in some places, the Eastern Continental Divide, the BRP does quite nicely. I would avoid it on weekends from the present right through October, (hordes of leaf-peepers) but it's a great way to get from Peak A to Peak B, since most of the Southern Appalachians' highest (Mount Rogers and Whitetop being notable exceptions) are either on it or are very close to it.
Be aware, Stew, that the GSMNP is closed just like SNP is. US 441 through Newfound Gap is open, but all roads off of it and otherwise accessing the Park are closed. There are some grumblings about the AT through the Park being closed, but no reports of hikers/backpackers being cited or otherwise hassled about being along the AT within GSMNP.
The weather in the Southern Appalachians can be severe, too. Nothing in the East tops Mt Washington for bad wx, but the 5,000-6,000 elevations in NC occasionally snag the lowermost layer of the jet stream, and sustained winds of 80-90 mph occur from time to time, with gusts up to 114 mph having been documented at 5,280' on Grandfather Mountain. Hurricane Sandy last year brought "wrap-around" winds and precip to the Southern Appalachians, to the tune of sustained 70-80mph winds and 24-30" of snow which proceeded to drift to 5-6' within GSMNP, marooning some AT southbounders who foolishly entered the Park when anybody with a brain knew better.
It seems as though you have a lengthy trip planned. If you like that kind of thing, look at a half-day's bicycle ride along the Virginia Creeper Trail, a rails-to-trails facility running from Whitetop Gap, VA, through Damascus, VA, to Abingdon, VA. The segment from Whitetop Gap to Damascus is 17 miles and all downhill, losing about 2,000' along the way. There is a small cafe' at Taylor's Valley featuring the world's best chocolate cake, and the trail is nice and smooth, running mostly along narrow gorges and their hosted mountain streams, with at least a couple dozen trestles, 3 of them being 50-100' above the stream. Like the BRP, I'd avoid the VCT on weekends in October, particularly Saturdays, but a midweek ride on a fair weather day is a terrific way to see the Blue Ridge up close and personal. I recommend Blue Blaze Bike Rental and Shuttle Service in Damascus. A nice sit-up-straight Trek Navigator 21-speed fat tire rental and a van shuttle ride up to Whitetop Gap will run you just shy of $30, and the trail takes you directly back to the Blue Blaze shop. Door to door will take you around 3.5 hours, with 2.75 or so being on the trail, stopping for a view, and scarfing that chocolate cake and a cup of coffee at Taylor's Valley. Damascus is a cool little outdoorsy "trail town" too, with the AT running right down Main Street. They bill themselves as "Trail City, USA" as a matter of fact.
Foy