Is the insurance company liable to pay damages to any cars that were hit during an accident when the person had a DUI?

If you mean, "Is the insurance carrier for the at-fault driver liable to pay if the at-fault driver received a DUI," the answer is almost always "yes." The at-fault DUI driver might have a provision in his or her policy that would exclude coverage for this type of accident, but I've never seen it. And even if such a provision did exist, it's unlikely a court would uphold it because it's against public policy to place injured parties -- not to mention the drunken insured -- in a situation where they aren't indemnified. The at-fault DUI driver is in for a nasty surprise, though, when he sees what his premiums are going to be for the next few years...