Yes, if a gene's surrounded by copies of itself, then there might be certain scenarios where it will destroy a copy of itself to help other copies of the same gene.
For example apoptosis happens all the time in human cells. If a cell believes it's infected by a virus or a cancerous mutation, it will voluntarily destroy itself. That's because its continued existence threatens its genetically identical cellular neighbors. Thus genetic inclusive fitness is maximized.
But what absolutely wouldn't happen is such self-sacrifice on a species wide level. Two random members of a species are not closely enough related for self-sacrifice to maximize inclusive genetic fitness. Almost certainly a non-complying free rider mutation would arise in one or more individuals, and exploit the other species' members altruism.
The hypothesis was that aging evolved as an adaptation to accelerate the evolution of the species. To see the absurdity of this hypothesis, consider that if this logic held, then mate guarding would definitely not exist. In fact just the opposite, males would routinely solicit the highest-quality males they could find to mate with their females. And be happy about it. After all this would also accelerate species wide evolution, at the expense of individual fitness.