By "continuous physics", it doesn't mean the "objects don't go through walls" thing (that's easy), it means that it actually finds the times that interactions happen. Box2d isn't able to use that in all cases, but it does allow it to act the same way as a tickless simulation if your game's physics is simple enough, like 2d platformers.
I think theoretically you're correct that the methods underlying Box2d could be used in such a way, but practically I don't think it's there, as that was never one of the engine's goals. Read up on the methods used (for instance, http://twvideo01.ubm-us.net/o1/vault/gdc2013/slides/824737Ca...) for some of the limitations that Erin chose to accept. In particular the fact that it misses multiple roots during the solve means that you can't use if for perfect tickless simulation; there are (were? I'm not sure to what extent they've been addressed since I was deep in that code) also issues with conservation of time that would be a problem, which are discussed elsewhere (for instance http://box2d.org/forum/viewtopic.php?t=154).
