A better etymologist would probably know more than me, but I don’t believe so.
Rapeseed comes from the Latin Rapa/rapum, which means “turnip”. The family that rapeseed belongs to is the Brassicaceae, or turnip family, and the top of the plant (though not the root) resembles the turnip, so the name makes sense. It’s been known as “rapeseed” or “oilseed rape” in English since at least the 14th/15th century.
By the way, its oil is also known as canola oil in most English-speaking countries, since people don’t like seeing “rape” in a name…
Broom rape, on the other hand, has a scientific name that means “strangling vetch”. The Broom family of plants was once known as “vetch”.
Given that the original definition of rape (from the Anglo-French rapir) was “to take by force, to abduct, to seize”, “Strangling vetch” can be reasonably transcribed to “broom rape”.
As such, I assume that “broom rape” really does mean a sort of terrible thing, even if that terrible thing is happening to a plant and doesn’t involve an actual broom, per se.
Humans have been out to get each other since before we were even Homo sapiens sapiens. For the strong and the brash, there was always outright physical violence; a club to the head or a knife to the throat was a simple way to destroy an unsuspecting rival.
But humanity had more than just violence at its disposal. Those inclined to plan and use their brains over their brawn found that there was an easier way to kill, one that would not risk their own body in an attack, or let others know who killed their rival, or even if the rival was killed by another person in the first place.
Enter: POISONS. Historically largely derived from plants, humans have murdered each other, and at times themselves, using various species of plants. There is an expansive list of plants that can potentially kill a human, but a few have gained reputations over the millenia as premier agents of death…
A Modern Herbal. Mrs. M. Grieve, 1931.
Plants and Civilization. Maintained by Prof. Arthur C. Gibson, from 1985 textbook.