Depends on the airline. Check the exact luggage allowances for your flight. You might have a piece limit, a weight limit or both. You're going to have to figure out how to configure your stuff based on that.

Definitely plan on the airline opening your bike box and maybe not getting it back together that well. I don't like to stuff a bunch of things in with my bike for this reason. You want to make it easy on the luggage handlers so that they are easy on your bike. Zip tie or tape together any loose stuff inside your bike box to your bike - like the rack pieces, bags of parts, saddle, etc. that you had to remove to get the bike in there. I might put a thermarest or tent in there if I have to, but not a whole bunch of stuff. You don't want the luggage handlers to consider your box a pain in the butt.

I have a very light weight duffel bag that I put all my panniers and tent etc. into, as my 2nd peice of luggage. I keep the handlebar bag with me as my "purse" and one pannier or stuff sack as carryon, to get it all to fit into the luggage limit. Make sure not to try to carry on anything the airlines don't like as carryon - knives, etc. On the other end I just take out my panniers, and stuff the duffle bag inside, and carry it with me. If you are starting/ending your bike trip at the same place, you might be able to convince a hotel or hostel to hang onto your bike box and duffel bag for the duration of your ride.

I have used straps to lash my panniers together on other trips, too, instead of the duffel, but they don't stay toghether that well.

I also shop for food and fuel at my desination, you can get that stuff anywhere, so that helps keep you under the weight limit.

Have fun...

Anna