Sorry I am so late to respond - I live near Asheville, so I am familiar with a good amount of the parkway.
Cell reception is notably poor on the parkway - don't count on it - especially in the highest elevations near Water Rock Knob and Mitchell. Do ride up to Mitchell - it is a nice little side trip.
You should be fine with your 27 in the back - you won't find anything on the parkway double digit steep - climbs are long though - several miles.
Tunnels - some are bad (btwn Cherokee and Asheville) - a light is a must. Also the rangers are really quick to ticket you if you don't have one on the back, or if they see you riding two or more abreast, and NO NATURE BREAKS in view of the parkway - that will get you a big fat fine.
Be careful with the temps - I was up on the parkway a week ago for the Blue Ridge Breakaway ride and they had to evacuate people off the parkway due to hypothermia - and the fog and rain were really really bad as well - fog has no season it seems.....
Traffic on the parkway will ususally be light - unless as someone mentioned you are near Asheville during the commuter rush. I have not had any bad experiences on the parkway, which is more than I can say once you get off it.
Regarding side trips off the parkway - usually you are not near much "civilization" and you have to ride downhill several miles for services off the parkway (asheville being the exception) Liberty Bikes is a great bike shop right off the parkway in Asheville - they are very friendly and helpful there. Another nice little area to stop in and not hard to get back onto the parkway is down davidson river road to pisgah forrest (brevard, NC) - another good bike shop here and good places to eat. Little Switzerland is over-rated in my opinion.
Sounds like a wonderful ride - be safe and have a great time.