The short answer is apparently yes but the details are quite hazy. What even is rapeseed in the first place? The Cambridge World History of Food says:
The term “rapeseed” is used for any oil-bearing Brassica seed, including that of mustard.
The genus Brassica includes a long list of common vegetables from broccoli and bok choi to cabbage and turnips, and there are several known hybrids between species. Some sources seem to reserve the term rapeseed for specific oilseed cultivars but it's often unclear.
The Cambridge World History mentions that the "use of rapeseed oil for food and illumination originated in Asia (later spreading to the Mediterranean and Europe)" but provides no further details or references.
An article titled simply "History, Origin, and Evolution" focuses on India and claims (in rather convoluted English):
Two species, B. juncea and B. campestris having a range of morphotypes, are the crops of antiquity in India where much before the Christian era, they were used for many purposes including oil for cooking and frying, spice for seasoning food articles, vegetables, and for religious ceremonies (Mehra, 1966).
The term "rape" is related to turnips or Brassica rapa, whose morphotypes include both turnips and oilseed crops. Canola, popular for cooking oil today, is a cross of Brassica rapa and Brasica napa developed in the 1970s.
In a comment, JustCal links to an article that includes a detailed paragraph on the history of Brassica crops in China. It's clear that several were considered oilseed crops in ancient times, but there is nothing there about whether the oil was consumed as food.
There's an interesting account from 16th century Europe:
In Germany, a comprehensive account of winter rapeseed production
in the Rhineland area dates from 1570 with the oil being used as a lamp oil, a cheaper alternative to olive oil, and as a cooking fat in “a poor man’s kitchen.”
I've seen this attributed to Heresbach but I've not found the exact reference, nor have I seen any guesses on what species this might have been.
Overall, I think it's safe to say that oils of various Brassica species have been consumed in various times and places. If you want to know about any particular species, the story may be difficult to trace.
documentation of its use in India 4,000 years ago, and use in China and Japan 2,000 years ago
with a footnote on the source, and other sources are easily found. The linguistic question will require someone with language skills but I would consider it off-topic.