No. I would agree that this is one of at least three things that it might mean. I was contemplating picking on “unlawfully” in that section as another illustration of the inconsistent way in which the code is drafted, which makes it difficult to know what it's saying.
There are sections in the Criminal Code where “unlawfully” means exactly what you are saying, like section 269, “unlawfully causing bodily harm”. In that sense, it does add that there must have been some other offence committed. In some sections, “unlawfully” seems to mean something like “without lawful excuse”. The trouble is that the code uses the phrase “without lawful excuse” dozens of times, so it's not as though the drafters didn't know that the phrase “without lawful excuse” is a good way to capture the meaning “without lawful excuse”. If that's what it means, why say “unlawfully”?
There are some sections of the Criminal Code where words like “unlawfully”, “corruptly”, or “dishonestly” actually just seem to be some kind of expression of opinion or disapprobation. There is the offence of a justice official “corruptly” accepting a bribe. As far as I can tell, the word “corruptly” actually isn't doing any work. What's the non-corrupt way to accept a bribe?
These are the kinds of things that have been just sort of randomly scattered in the code as a means of tripping us up and preventing us from being sure of what it means. Yes, “unlawfully” might mean what you said, but there are at least two other things it might mean as well.