In most cases, the answer is no. It is generally not worth your time to negotiate with the insurance company before pursuing a lawsuit.
Insurance companies know what they are doing and they are skilled at finding ways to avoid paying on claims. The insurer will use the pre-suit negotiation to obtain as much information about you, your lawyer and your experts, as possible.
We believe it is almost always a waste of time to attempt to negotiate with the insurance company before filing suit. Instead we usually file the lawsuit first, so that if negotiations break down, we already have a trial date set.