Would 我一看这很容易的课就懂了。 be correct?
The sentence is grammatical, However, 这课我一看就懂 already indicated you think it is easy, adding "很容易的" make the sentence unnecessarily wordy.
You can add relative clauses in any part of the sentence as long as it makes sense:
这油画我一看就知是假的
这(标价三千万的)油画,我一看就知是假的
这油画(用的是二十世纪才有的油彩),一看就知是假的
这油画,(身为画家的)我一看就知是假的 -