Very unlikely. Keep in mind that most of what this attachment does is keep the rack upright. It will take some of weight, but most of the weight will be on lower rack mounts. Although if your bike lacks upper rack mounts, does it have lower rack mounts?

On my wife's bike, I threaded the rack supports right through the quick-release of the seatpost clamp. Always meant to get one of those, but never got around to it, but she never had a problem. She never did any loaded touring, either.