I would not recommend it. The insurance adjuster and/or defense attorney will exploit your inability to properly articulate and convincingly argue the strengths of your case. The inspiration for this post comes from Jonathan Stein, a California personal injury attorney who has a great post on his blog about this very topic. Here is his post:

FAQ: Can I mediate my own case?

Simple answer: Yes.

Sure, you can. But why would you? I could stitch up my own cut, but I don’t. Why? Primarily because it is worthwhile to have an professional do it. This is no different. You can do this yourself but you are better off with an professional there – someone who does this for a living.

As I tell all of my clients: I don’t practice medicine (or accounting or teach or well, you get the idea), so I won’t tell their doctor (or accountant or teacher) what to do. At the same time, they don’t practice law, so I don’t want them telling me what to do. Why? Because you need a certain amount of experience to do these things.

Hire an professional if you are going to do something like this.