Neither. "This makes no sense" means that the speaker cannot construct a rational argument as to why the particular situation (whatever "this" is) should be true or reasonable, and in particular contends that it is false or unreasonable.
"We'll go tomorrow."
"That makes no sense; the shop is closed tomorrow!"
ETA: this is quite a strong statement, so you had better be able to back it up if you don't want to cause offense!
The latter I would consider to be the more normal these days.
Can this "come with" mean such an abstract idea?
Yes, as Spider-Man learns, "with great power comes great responsibility", which is far from the only example (or the original wording, just to pre-empt any comic-book pedants, though I'll note the original used there), but it is one such example of the "with … comes …" form with an abstract noun.