The short answer to your question is, Yes!
The answer you are looking for is below.
In order to get my point across I will minimize Fixed Price Contract and Agile definitions.
In my own words, Agile methodology is nothing more than having short burst of full development cycles to ease the anxiety of the customer. Sorry that I am minimizing such a great platform in these words, but in essence, the reason it exists, is because with previous methodologies the customer was surprised too often.
Now, a fixed price contract is the contract that has a set scope, and the vendor has 100% the Risk (in most cases) of making sure he estimates before signing the contract with the buyer.
You can "easily" (nothing is easy) break the scope of the FPC in 1-n sprints, and use agile to work through it. Having a very minimal product always ready to be presented to the customer. This will make Agile and FPC work together.
I will go a step more to say, I have never done this myself, but I think this combination could be a winner, for the vendor to identify risk in his side early on, so that he can minimize any loss.
I hope this helps you.