The mainy thing that really maters is whether you can ride the bike comfortably. There is a case against flat bars, but folks who have racked up 100s of thousands of miles use them exclusively, so while I prefer drops on the road, it's not the only view.
28 spoke wheels, with no racks should be fine, I'm big and have run 32s without a problem. I don't thrash a bike, I'm not out there to do bunny hops or cliff drops, if your terrain requires that, you might have a problem, but rolling on worn paved roads without a rack.
Heck if you can switch out your bike in favour of a better one for your trip, go for it, but I think you can make it if you can't.
Check this out about a pro bike and hike trip, walmart bikes,
http://www.rayjardine.com/adventures...03-iua-1.shtml