It all depends on what car seat was involved and what that specific manufacturer has for replacement criteria. Unless the seat involved was a Britax, chances are it's going to have to be replaced, no matter how slow or minor the crash was.
Britax says you can re-use a child seat after a minor crash if it fits ALL of NHTSA's criteria:
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Minor crashes are those that meet ALL of the following criteria:
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The vehicle was able to be driven away from the crash site;
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The vehicle door nearest the safety seat was undamaged;
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There were no injuries to any of the vehicle occupants;
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The air bags (if present) did not deploy; AND
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There is no visible damage to the safety seat
Most other manufacturers require replacement after ANY crash...which means, well, ANY crash. So, whether or not insurance will pony up, the seat needs to be discarded immediately and replaced. Insurance companies don't, typically, give trouble with replacement coverage (though, yes, some do...), especially with documentation from the manufacturer expressing replacement requirements (like a manual).