I am really interested in hiking a trail like this.. if you have any experience let me know how it went! Did you feel PALEO?? haha
I'm "sectional through-hiking" which means I'm slowly hiking each section as I can, since I can't get 5 or 6 months away from work and the family to do it all at once. I've only covered about 400 miles so I figure another 20-25 years and I'll be done since I typically get out for 70-100 miles once or twice a year. :-)
Alternatively, I'm hopeful one of my kids will want to do the whole thing someday so I'll have a good excuse to go too.
It's a great experience, and I recommend hanging out on whiteblaze.net for a while to get a feel for what backpacking is all about both in general and more specifically for a through hike.
Now, if you want to EAT paleo on a through hike, I think it would be tough. Hard to keep up on fresh veggies and meat when you don't see re-supply for 4 or 5 or more days. And most of the dehydrated foods are not Paleo like at all. It would most likely be best to prepare your own freeze dried food before hand to get closer to paleo than other pre-made products.
When I backpack I still may go for gluten-free oatmeal in the morning, knowing that I'll be burning off the sugar spike pretty much as it occurs. Beyond that I've recently created trail mixes of macadamia nuts, coconut flakes, cashews, and some dried fruit. Jerky works, and salami will last a day or two or three after you open it depending on the weather.
Other ideas would be nut butters and honey, I still eat cheese occasionally so I take a block along, carry a bit of olive oil to mix in with salmon and tuna packs, and that kind of thing. Variety may be hard to come by depending on how strict you want to be. I personally don't want to be eating pemmican and jerky the whole time. :-)
I've section hiked quite a bit of the PCT- it's AWESOME and yes there is definitely a potential to 'feel' Paleo- especially when jumping into an ice cold sierra lake is your morning "shower".
On the other hand it's a major commitment and represents a lot of planning that is made more challenging by the need to limit yourself to Paleo foods.
That said, I firmly believe that It can be done full Paleo and that will enjoy it that much more! It just takes a bit more planning and determination. I make a lot of my own foods for longer (week plus to month long) hikes and you can also buy a lot more Paleo friendly hiking foods nowadays- see my response to Lars at http://paleohacks.com/questions/44488/food-for-mountain-hiking/44600#44600 for some brief suggestions.
If you decide to do the PCT I'd recommend checking out the PCT or JMT yahoo groups. (JMT=John Muir Trail-220 mi of the prettist section of the PCT in the Sierras) they've got great info on the nitty gritty of planning for your trip.
I'm also playing with the idea of putting together a site focusing on backcountry paleo- including food and overall trip planning. Seems like there might be a need. :)
I did three days/nights on the AT with a couple college pals a few years ago and it was one of my favorite weekends of all time. We hiked a section from the souther part of Virginia into North Carolina and it was beautiful.
We used a combination of trail shelters (which was cool because we got to hang out and share a fire with random people) as well as breaking camp from our own packs.
Really, I can't express how awesome it was and if you can get a couple of good friends together I recommend you just go, even if it is for a long weekend.