No. One of the reasons you fly first class is to make sure you don’t get included in a “lottery” in a situation like that.
Actually there was a story from a business owner who paid $1000 for first class back from Hawaii to California. He was sitting in his first class seat sipping orange juice when they gave him the bad news that the algorithm said there was a higher level first class customer who needed the seat and he would have to leave. He resisted they threatened to put him in handcuffs. He finally got them to refund $500 so he could sit in a middle seat in the back.