Is it worth adding story points as a commitment when preparing a fixed price contract for agile project.

How are story points ever achieved? There is no value in them. Moreover,  it doesn't sound as though people are being foolish enough to look for value there in the first place. Instead it seems they are wise enough to flex scope, so they learn to build the right thing at the right time. The delivery of those Done increments is where value will surely lie.

Encourage the Developers to commit to the quality of the increments they provide, and to attainable goals which mitigate significant risks and unknowns. Let them use estimates for the purpose they are intended: to help them get their arms around how much work they can take on each Sprint so these meaningful commitments are achieved.

Story Points guesses based upon information available at a particular point in time.  As work begins on something, new information is obtained and the original guesses are no longer valid.  Why would you put any kind of metric about that in a contract? 

I like @Ian's question on achieving story points.  There is nothing there to achieve.  Think of it this way.  You tell your spouse that you are going to the grocery market and will be back in 2 hours.  You start your journey and find that a road is closed due to a sinkhole forming in the roadway. You take an alternate route.  Partway through that route, you find that another road has been closed because of a large accident. You take yet another alternate route.  You finally arrive at the market and find that it is very crowded.  It takes you longer to make your way through the store to gather your items than you expected due to the number of people.  Same happens when you try to pay for your purchases.  You finally get out of the market and start home.  You remember the road closings and decide to take another route to your home.  Part way through that route, you find another road closure due to a local celebration.  Once again you vary your route.  You finally make it home.  It has been 4.5 hours since you left home.  Your spouse says that since it took your 2.5 hours longer than you said it would there will be no dinner that evening. 

How would you expect the company that is paying for the contract to react when you say the team will do 20 story points each sprint but they can only complete 15 for the first 3 sprints?   

Now consider that you state there will be a increment of value created and discussed with the client every Sprint.  The client sees that is met and in some cases there are more than one increment provided.  

Which would the customer appreciate more?  A number of story points or valuable increments?

Ian and Daniel's comments are both very good. I'll add one thing.

If you are using a fixed budget effort using Scrum, schedule is also fixed. If you have a Scrum Team, that team has a (roughly) fixed cost per Sprint. It may change slightly for things like team members taking time off or the team needing a subject matter expert from outside the team. But based on the cost of the Scrum Team and a chosen Sprint length, you can figure out how many Sprints you can achieve.

I'd say that is more valuable. Once you start Sprinting, you can monitor throughput and cycle time in addition to demonstrating value every Sprint. Between these things, there can be informed decisions about ordering the Product Backlog to maximize value before the money runs out and the customer can make informed decisions about if they want to add more money to get more Sprints to further develop the product.

None of this requires story points, which don't mean anything to your customers or even your internal stakeholders. It's all about demonstrating the team's ability to deliver value and forecasting how long it will take to complete certain items in the Product Backlog based on past performance.