One thing though DO NOT put anything else in the bag or you do risk trouble.
No one has ever checked this. I'm assuming that it gets picked up as the bike goes through X-Ray but no-one has ever said "remove all that stuff".
Everything goes in my bike bag. Clothing, helmet, shoes, tools, spares, Camelbak and then I only have carry on baggage.
Always take a copy of the T&C's with the relevant sections highlighted, it helps avoid arguments if there's any problems with the weight (mine has never been over 32kg even with all the stuff in there).