Demonmonkey,
Perhaps the sentiment came across poorly, so let me try and redeem myself.
The question is analogous to one of "If I take out a mortgage and interest rates fall will I be able to take advantage of those falls?" The answer would depend on the type of mortgage contract you had taken out, such as fixed, capped, tracker, capped and collared, or variable. In other words, "it all depends."
"Hedging," incorporates a variety of strategies and contracts, that the term is used as a wrapper for. For example Futures contracts, swap contracts, call options and collars. The flexibility and penalty risk of each type of contract varies considerably, and an airline may very well employ a mix of these contracts to mitigate it's risk.
It is difficult to answer your question as the answer would depend on the type of the contract. Some contracts can be deferred. At the risk of pointing you back out into the internet, there is a video article
Here that may be of interest to you? The follow on article is
Here.
The problem (as I have also discovered researching this subject) is that as with many types of derivative trading, the subject is complex. Hedging is a general term used to encompass a variety of different strategies, and the answer to questions often depends on the strategy employed.