Sorry, you've lost me at the code :)
If I understand it correctly from your first sentence, are you checking the distance between Obj A and Obj B and then seeing if the distance is less than their respective widths/heights?
If so, then how would you handle rotation? Maybe it'd be easier to just not do it and pretend everything is a sphere/circle so you'd just check in a radius around it?
Anyhow, that's an interesting approach; I think I'll stick with raycasts, even if they are more resource intensive, simply because they're easier, but do let me know how it work out!